Skip to main content Accessibility help
×
Home
Cubical Homotopy Theory
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 6
  • Export citation
  • Recommend to librarian
  • Buy the print book

Book description

Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological spaces with an emphasis on cubical diagrams. The book contains 300 examples and provides detailed explanations of many fundamental results. Part I focuses on foundational material on homotopy theory, viewed through the lens of cubical diagrams: fibrations and cofibrations, homotopy pullbacks and pushouts, and the Blakers–Massey Theorem. Part II includes a brief example-driven introduction to categories, limits and colimits, an accessible account of homotopy limits and colimits of diagrams of spaces, and a treatment of cosimplicial spaces. The book finishes with applications to some exciting new topics that use cubical diagrams: an overview of two versions of calculus of functors and an account of recent developments in the study of the topology of spaces of knots.

Reviews

'… this volume can serve as a good point of reference for the machinery of homotopy pullbacks and pushouts of punctured n-cubes, with all the associated theory that comes with it, and shows with clarity the interest these methods have in helping to solve current, general problems in homotopy theory. Chapter 10, in particular, proves that what is presented here goes beyond the simple development of a new language to deal with old problems, and rather shows promise and power that should be taken into account.'

Miguel Saramago Source: MathSciNet

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Contents

References
[AC11] Gregory, Arone and Michael, Ching. Operads and chain rules for the calculus of functors. Astérisque, (338):vi+158, 2011.
[AC14] Gregory, Arone and Michael, Ching. Cross-effects and the classification of Taylor towers. arXiv:1404.1417, 2014.
[AC15] Gregory, Arone and Michael, Ching. A classification of Taylor towers of functors of spaces and spectra. Adv. Math., 272:471–552, 2015.
[AD01] G. Z., Arone and W.G., Dwyer. Partition complexes, Tits buildings and symmetric products. Proc. London Math. Soc. (3), 82(1):229–256, 2001.
[Ada78] John Frank, Adams. Infinite loop spaces. Annals of Mathematics Studies, Vol. 90. Princeton University Press, Princeton, NJ, 1978.
[AGP02] Marcelo, Aguilar, Samuel, Gitler, and Carlos, Prieto. Algebraic topology from a homotopical viewpoint. Universitext. Springer-Verlag, New York, 2002. Translated from the Spanish by Stephen Bruce Sontz.
[AK02] Stephen T., Ahearn and Nicholas J., Kuhn. Product and other fine structure in polynomial resolutions of mapping spaces. Algebr. Geom. Topol., 2:591–647 (electronic), 2002.
[ALTV08] Greg, Arone, Pascal, Lambrechts, Victor, Turchin, and Ismar, Voli´c. Coformality and rational homotopy groups of spaces of long knots. Math. Res. Lett., 15(1):1–14, 2008.
[ALV07] Gregory, Arone, Pascal, Lambrechts, and Ismar, Voli´c. Calculus of functors, operad formality, and rational homology of embedding spaces. Acta Math., 199(2):153–198, 2007.
[AM99] Greg, Arone and Mark, Mahowald. The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres. Invent. Math., 135(3):743–788, 1999.
[And72] D.W., Anderson. A generalization of the Eilenberg–Moore spectral sequence. Bull. Amer. Math. Soc., 78:784–786, 1972.
[AP99] M. A., Aguilar and Carlos, Prieto. Quasifibrations and Bott periodicity. Topology Appl., 98(1–3):3–17, 1999. (II Iberoamerican Conference on Topology and its Applications (Morelia, 1997)).
[Ara53] Shôrô, Araki. On the triad excision theorem of Blakers and Massey. Nagoya Math. J., 6:129–136, 1953.
[Ark62] Martin, Arkowitz. The generalized Whitehead product. Pacific J. Math., 12(1):7–23, 1962.
[Ark11] Martin, Arkowitz. Introduction to homotopy theory. Universitext. Springer, New York, 2011.
[Arn69] V. I.|Arnol d. The cohomology ring of the group of dyed braids. Mat. Zametki, 5:227–231, 1969.
[Aro99] Gregory, Arone. A generalization of Snaith-type filtration. Trans. Amer. Math. Soc., 351(3):1123–1150, 1999.
[Aro02] Gregory, Arone. The Weiss derivatives of BO(−) and BU(−). Topology, 41(3):451–481, 2002.
[AS94] Scott, Axelrod and I.M., Singer. Chern-Simons perturbation theory. II. J. Differential Geom., 39(1):173–213, 1994.
[AT14] Gregory Arone and Victor Turchin. On the rational homology of high-dimensional analogues of spaces of long knots. Geom. Topol., 18(3):1261–1322, 2014.
[Bat98] Mikhail A., Batanin. Homotopy coherent category theory and A∞-structures in monoidal categories. J. Pure Appl. Algebra, 123(1–3):67–103, 1998.
[BB10] Hans Joachim, Baues and David, Blanc. Stems and spectral sequences. Algebr. Geom. Topol., 10(4):2061–2078, 2010.
[BCKS14] Ryan, Budney, James, Conant, Robin, Koytcheff, and Dev, Sinha. Embedding calculus knot invariants are of finite type. arXiv:1411.1832, 2014.
[BCM78] M., Bendersky, E.B., Curtis, and H. R., Miller. The unstable Adams spectral sequence for generalized homology. Topology, 17(3):229–248, 1978.
[BCR07] Georg, Biedermann, Boris, Chorny, and Oliver, Röndigs. Calculus of functors and model categories. Adv. Math., 214(1):92–115, 2007.
[BCSS05] Ryan, Budney, James, Conant, Kevin P., Scannell, and Dev, Sinha. New perspectives on self-linking. Adv. Math., 191(1):78–113, 2005.
[BD03] Martin, Bendersky and Donald M., Davis. A stable approach to an unstable homotopy spectral sequence. Topology, 42(6):1261–1287, 2003.
[Beh02] Mark J., Behrens. A new proof of the Bott periodicity theorem. Topology Appl., 119(2):167–183, 2002.
[Beh12] Mark, Behrens. The Goodwillie tower and the EHP sequence. Mem. Amer. Math. Soc., 218(1026):xii+90, 2012.
[BJR15] Kristine, Bauer, Brenda, Johnson, and McCarthy, Randy. Cross effects and calculus in an unbased setting (with an appendix by Rosona Eldred). Trans. Amer. Math. Soc., 367(9):6671–6678, 2015.
[BK72a] A.K., Bousfield and D.M., Kan. Homotopy limits, completions and localizations. Lecture Notes in Mathematics, Vol. 304. Springer-Verlag, Berlin, 1972.
[BK72b] A. K., Bousfield and D.M., Kan. The homotopy spectral sequence of a space with coefficients in a ring. Topology, 11:79–106, 1972.
[BK73] A. K., Bousfield and D.M., Kan. A second quadrant homotopy spectral sequence. Trans. Amer. Math. Soc., 177:305–318, 1973.
[BL84] Ronald, Brown and Jean-Louis, Loday. Excision homotopique en basse dimension. C. R. Acad. Sci. Paris Sér. I Math., 298(15):353–356, 1984.
[BL87a] Ronald, Brown and Jean-Louis, Loday. Homotopical excision, and Hurewicz theorems for n-cubes of spaces. Proc. London Math. Soc. (3), 54(1):176–192, 1987.
[BL87b] Ronald, Brown and Jean-Louis, Loday. Van Kampen theorems for diagrams of spaces. With an appendix by M. Zisman. Topology, 26(3):311–335, 1987.
[BM49] A. L., Blakers and William S., Massey. The homotopy groups of a triad. Proc. Nat. Acad. Sci. USA, 35:322–328, 1949.
[BM51] A. L., Blakers and W. S., Massey. The homotopy groups of a triad. I. Ann. Math. (2), 53:161–205, 1951.
[BM52] A. L., Blakers and W. S., Massey. The homotopy groups of a triad. II. Ann. Math. (2), 55:192–201, 1952.
[BM53a] A. L., Blakers and W. S., Massey. The homotopy groups of a triad. III. Ann. Math. (2), 58:409–417, 1953.
[BM53b] A. L., Blakers and W. S., Massey. Products in homotopy theory. Ann. Math. (2), 58:295–324, 1953.
[BN95] Dror, Bar-Natan. On the Vassiliev knot invariants. Topology, 34(2):423–472, 1995.
[BO05] Marcel, Bökstedt and Iver, Ottosen. A spectral sequence for string cohomology. Topology, 44(6):1181–1212, 2005.
[Boa71] J. M., Boardman. Homotopy structures and the language of trees. In Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970), pp. 37–58. American Mathematical Society, Providence, RI, 1971.
[Bor94] Francis, Borceux. Handbook of categorical algebra, Vol. 1. Encyclopedia of Mathematics and its Applications, Vol. 50. Cambridge University Press, Cambridge, 1994.
[Bou87] A. K., Bousfield. On the homology spectral sequence of a cosimplicial space. Amer. J. Math., 109(2):361–394, 1987.
[Bou89] A. K., Bousfield. Homotopy spectral sequences and obstructions. Israel J. Math., 66(1–3):54–104, 1989.
[Bou03] A. K., Bousfield. Cosimplicial resolutions and homotopy spectral sequences in model categories. Geom. Topol., 7:1001–1053 (electronic), 2003.
[Bre93] Glen E., Bredon. Topology and geometry. Graduate Texts in Mathematics, Vol. 139. Springer-Verlag, New York, 1993.
[Bro68] Ronald, Brown. Elements of modern topology. McGraw-Hill, New York, 1968.
[BT82] Raoul, Bott and Loring, W. Tu.Differential forms in algebraic topology.Graduate Texts in Mathematics, Vol. 82. Springer-Verlag, New York, 1982.
[BT00] Martin, Bendersky and Robert D., Thompson. The Bousfield–Kan spectral sequence for periodic homology theories. Amer. J.Math., 122(3):599–635, 2000.
[Bud07] Ryan, Budney. Little cubes and long knots. Topology, 46(1):1–27, 2007.
[Bud08] Ryan, Budney. A family of embedding spaces. In Groups, homotopy and configuration spaces. Geometry and Topology Monographs, Vol. 13, pp. 41–83. Mathematical Science Publishers, Coventry, 2008.
[Bud10] Ryan, Budney. Topology of spaces of knots in dimension 3. Proc. London Math. Soc. (3), 101(2):477–496, 2010.
[BV73] J. M., Boardman and R. M., Vogt. Homotopy invariant algebraic structures on topological spaces. Lecture Notes in Mathematics, Vol. 347. Springer-Verlag, Berlin, 1973.
[BW56] M. G., Barratt and J.H. C., Whitehead. The first nonvanishing group of an (n + 1)-ad. Proc. London Math. Soc. (3), 6:417–439, 1956.
[CCGH87] G. E., Carlsson, R. L., Cohen, T., Goodwillie, and W. C., Hsiang. The free loop space and the algebraic K-theory of spaces. K-Theory, 1(1):53–82, 1987.
[CCRL02] Alberto, S. Cattaneo|Paolo Cotta-Ramusino, and Riccardo, Longoni. Configuration spaces and Vassiliev classes in any dimension. Algebr. Geom. Topol., 2:949–1000 (electronic), 2002.
[CDI02] W., Chachólski, W. G., Dwyer, and M., Intermont. The A-complexity of a space. J. London Math. Soc. (2), 65(1):204–222, 2002.
[CDM12] S., Chmutov, S., Duzhin, and J., Mostovoy. Introduction to Vassiliev knot invariants. Cambridge University Press, Cambridge, 2012.
[Cha97] Wojciech, Chachólski. A generalization of the triad theorem of Blakers– Massey. Topology, 36(6):1381–1400, 1997.
[Chi05] Michael, Ching. Bar constructions for topological operads and the Goodwillie derivatives of the identity. Geom. Topol., 9:833–933 (electronic), 2005.
[Chi10] Michael, Ching. A chain rule for Goodwillie derivatives of functors from spectra to spectra. Trans. Amer. Math. Soc., 362(1):399–426, 2010.
[Cho] Boris, Chorny. A classification of small linear functors. arXiv:1409.8525, 2014.
[CLM76] Frederick R., Cohen, Thomas J., Lada, and J. Peter, May. The homology of iterated loop spaces. Lecture Notes in Mathematics, Vol. 533. Springer-Verlag, Berlin, 1976.
[CLOT03] Octav, Cornea, Gregory, Lupton, John, Oprea, and Daniel, Tanré. Lusternik-Schnirelmann category, Mathematical Surveys and Monographs, Vol. 103. American Mathematical Society, Providence, RI, 2003.
[Coh73] Fred, Cohen. Cohomology of braid spaces. Bull. Amer.Math. Soc., 79:763– 766, 1973.
[Coh95] F. R., Cohen. On configuration spaces, their homology, and Lie algebras. J. Pure Appl. Algebra, 100(1–3):19–42, 1995.
[Con08] James, Conant. Homotopy approximations to the space of knots, Feynman diagrams, and a conjecture of Scannell and Sinha. Amer. J. Math., 130(2):341–357, 2008.
[CS02] Wojciech, Chachólski and Jérôme, Scherer. Homotopy theory of diagrams. Mem. Amer. Math. Soc., 155(736):x+90, 2002.
[DD77] E., Dror and W.G., Dwyer. A long homology localization tower. Comment. Math. Helv., 52(2):185–210, 1977.
[DF87] E. Dror, Farjoun. Homotopy theories for diagrams of spaces. Proc. Amer. Math. Soc., 101(1):181–189, 1987.
[DFZ86] E. Dror, Farjoun and A., Zabrodsky. Homotopy equivalence between diagrams of spaces. J. Pure Appl. Algebra, 41(2–3):169–182, 1986.
[DGM13] Bjørn Ian, Dundas, Thomas G., Goodwillie, and Randy, McCarthy. The local structure of algebraic K-theory. Algebra and Applications, Vol. 18. Springer-Verlag, London, 2013.
[DH12] William, Dwyer and Kathryn, Hess. Long knots and maps between operads. Geom. Topol., 16(2):919–955, 2012.
[DHKS04] William G., Dwyer, Philip S., Hirschhorn, Daniel M., Kan, and Jeffrey H., Smith. Homotopy limit functors on model categories and homotopical categories. Mathematical Surveys and Monographs, Vol. 113. American Mathematical Society, Providence, RI, 2004.
[DI04] Daniel, Dugger and Daniel C., Isaksen. Topological hypercovers and A1-realizations. Math. Z., 246(4):667–689, 2004.
[DK84] W. G., Dwyer and D.M., Kan. A classification theorem for diagrams of simplicial sets. Topology, 23(2):139–155, 1984.
[DL59] Albrecht, Dold and Richard, Lashof. Principal quasi-fibrations and fibre homotopy equivalence of bundles. Illinois J. Math., 3:285–305, 1959.
[DMN89] William, Dwyer, Haynes, Miller, and Joseph, Neisendorfer. Fibrewise completion and unstable Adams spectral sequences. Israel J. Math., 66(1–3):160–178, 1989.
[Dro72] Emmanuel, Dror. Acyclic spaces. Topology, 11:339–348, 1972.
[DS95] W. G., Dwyer and J., Spalinski. Homotopy theories and model categories. In Handbook of algebraic topology, pp. 73–126. North-Holland, Amsterdam, 1995.
[DT56] Albrecht, Dold and René, Thom. Une généralisation de la notion d' espace fibré. Application aux produits symétriques infinis. C. R. Acad. Sci. Paris, 242:1680–1682, 1956.
[DT58] Albrecht, Dold and René, Thom. Quasifaserungen und unendliche symmetrische Produkte. Ann. Math. (2), 67:239–281, 1958.
[Dug01] Daniel, Dugger. Universal homotopy theories. Adv. Math., 164(1):144– 176, 2001.
[Dwy74] W. G., Dwyer. Strong convergence of the Eilenberg–Moore spectral sequence. Topology, 13:255–265, 1974.
[EH76] David A., Edwards and Harold M., Hastings. Cech and Steenrod homotopy theories with applications to geometric topology. Lecture Notes in Mathematics, Vol. 542. Springer-Verlag, Berlin–New York, 1976.
[Eld08] Rosona, Eldred. Tot primer. Available at www.math.uni-hamburg.de/home/ eldred/, 2008.
[Eld13] Rosona, Eldred. Cosimplicial models for the limit of the Goodwillie tower. Algebr. Geom. Topol., 13(2):1161–1182, 2013.
[EML54] Samuel, Eilenberg and Saunders Mac, Lane. On the groups H(Π, n). II. Methods of computation. Ann. Math. (2), 60:49–139, 1954.
[ES87] Graham, Ellis and Richard, Steiner. Higher-dimensional crossed modules and the homotopy groups of (n + 1)-ads. J. Pure Appl. Algebra, 46(2-3):117–136, 1987.
[FM94] William, Fulton and Robert, MacPherson. A compactification of configuration spaces. Ann. Math. (2), 139(1):183–225, 1994.
[FN62] Edward|Fadell and Lee|Neuwirth. Configuration spaces. Math. Scand., 10:111–118, 1962.
[Fri12] Greg, Friedman. Survey article: an elementary illustrated introduction to simplicial sets. Rocky Mountain J. Math., 42(2):353–423, 2012.
[Gai03] Giovanni, Gaiffi. Models for real subspace arrangements and stratified manifolds. Int. Math. Res. Not., (12):627–656, 2003.
[Gan65] T., Ganea. A generalization of the homology and homotopy suspension. Comment. Math. Helv., 39:295–322, 1965.
[Geo79] Ross, Geoghegan. The inverse limit of homotopy equivalences between towers of fibrations is a homotopy equivalence – a simple proof. Topology Proc., 4(1):99–101 (1980), 1979.
[GG73] M., Golubitsky and V., Guillemin. Stable mappings and their singularities. Graduate Texts in Mathematics, Vol. 14. Springer-Verlag, New York, 1973.
[GJ99] Paul G., Goerss and John F., Jardine. Simplicial homotopy theory. Progress in Mathematics, Vol. 174. Birkhäuser Verlag, Basel, 1999.
[GK08] Thomas G., Goodwillie and John R., Klein. Multiple disjunction for spaces of Poincaré embeddings. J. Topol., 1(4):761–803, 2008.
[GK15] Thomas G., Goodwillie and John R., Klein. Multiple disjunction for spaces of smooth embeddings. arXiv:1407.6787, 2015.
[GKW01] Thomas G., Goodwillie, John R., Klein, and Michael S., Weiss. Spaces of smooth embeddings, disjunction and surgery. In Surveys on surgery theory, Vol. 2, ed. S., Cappell, A., Ranicki, and J., Rosenberg. Annals of Mathematics Studies, Vol. 149, pp. 221–284. Princeton University Press, Princeton, NJ, 2001.
[GM10] Thomas G., Goodwillie and Brian A., Munson. A stable range description of the space of link maps. Algebr. Geom. Topol., 10:1305–1315, 2010.
[Goe90] Paul G., Goerss. André-Quillen cohomology and the Bousfield-Kan spectral sequence. Astérisque, (191):6, 109–209, 1990. International Conference on Homotopy Theory (Marseille-Luminy, 1988).
[Goe93] Paul G., Goerss. Barratt's desuspension spectral sequence and the Lie ring analyzer. Quart. J. Math. Oxford Ser. (2), 44(173):43–85, 1993.
[Goe96] Paul G., Goerss. The homology of homotopy inverse limits. J. Pure Appl. Algebra, 111(1-3):83–122, 1996.
[Goo] Thomas G., Goodwillie. Excision estimates for spaces of diffeomorphisms. In preparation, available at http://www.math.brown.edu/ tomg/excisiondifftex.pdf
[Goo90] Thomas G., Goodwillie. Calculus. I. The first derivative of pseudoisotopy theory. K-Theory, 4(1):1–27, 1990.
[Goo92] Thomas G., Goodwillie. Calculus II: Analytic functors. K-Theory, 5(4):295–332, 1991/92.
[Goo98] Thomas G., Goodwillie. A remark on the homology of cosimplicial spaces. J. Pure Appl. Algebra, 127(2):167–175, 1998.
[Goo03] Thomas G.|Goodwillie. Calculus. III. Taylor series. Geom. Topol., 7:645–711 (electronic), 2003.
[Gra75] Brayton, Gray. Homotopy theory: An introduction to algebraic topology, Pure and Applied Mathematics, Vol. 64. Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1975.
[GV95] Murray, Gerstenhaber and Alexander A., Voronov. Homotopy G-algebras and moduli space operad. Internat. Math. Res. Notices, (3):141–153 (electronic), 1995.
[GW99] Thomas G., Goodwillie and Michael, Weiss. Embeddings from the point of view of immersion theory II. Geom. Topol., 3:103–118 (electronic), 1999.
[Hac10] Philip J., Hackney. Homology operations in the spectral sequence of a cosimplicial space. ProQuest LLC, Ann Arbor, MI, 2010. PhD thesis, Purdue University.
[Har70] K. A., Hardie. Quasifibration and adjunction. Pacific J. Math., 35:389–397, 1970.
[Hat02] Allen, Hatcher. Algebraic topology. Cambridge University Press, Cambridge, 2002.
[Hir15a] Philip S., Hirschhorn. Functorial CW-approximation. Available at www-math.mit.edu/psh/notes/cwapproximation.pdf, 2015.
[Hir15b] Philip S., Hirschhorn. The homotopy groups of the inverse limit of a tower of fibrations. Available at www-math.mit.edu/psh/notes/limfibra tions.pdf, 2015.
[Hir15c] Philip S., Hirschhorn. Notes on homotopy colimits and homotopy limits. Available at http://www-math.mit.edu/∼psh/notes/hocolim.pdf, 2015.
[Hir15d] Philip S.|Hirschhorn. The Quillen model category of topological spaces. Available at www-math.mit.edu/psh/notes/modcattop.pdf, 2015.
[Hir15e] Philip S., Hirschhorn. The diagonal of a multi-cosimplicial object. Available at www-math.mit.edu/ psh/diagncosimplicial.pdf, 2015.
[Hir94] Morris W., Hirsch. Differential topology. Graduate Texts in Mathematics, Vol. 33. Springer-Verlag, New York, 1994. Corrected reprint of the 1976 original.
[Hir03] Philip S., Hirschhorn. Model categories and their localizations. Mathematical Surveys and Monographs, Vol. 99. American Mathematical Society, Providence, RI, 2003.
[Hop] Michael J., Hopkins. Some problems in topology. PhD thesis, Oxford University, 1984.
[Hov99] Mark, Hovey. Model categories. Mathematical Surveys and Monographs, Vol. 63. American Mathematical Society, Providence, RI, 1999.
[JM99] Brenda, Johnson and Randy, McCarthy. Taylor towers for functors of additive categories. J. Pure Appl. Algebra, 137(3):253–284, 1999.
[JM04] B., Johnson and R., McCarthy. Deriving calculus with cotriples. Trans. Amer. Math. Soc., 356(2):757–803 (electronic), 2004.
[JM08] Brenda, Johnson and Randy, McCarthy. Taylor towers of symmetric and exterior powers. Fund. Math., 201(3):197–216, 2008.
[Joh95] B., Johnson. The derivatives of homotopy theory. Trans. Amer. Math. Soc., 347(4):1295–1321, 1995.
[KM02] Miriam Ruth, Kantorovitz and Randy, McCarthy. The Taylor towers for rational algebraic K-theory and Hochschild homology. Homology Homotopy Appl., 4(1):191–212, 2002.
[Koh02] Toshitake, ohno. Loop spaces of configuration spaces and finite type invariants. In Invariants of knots and 3-manifolds (Kyoto, 2001). Geometry and Topology Monographs, Vol. 4, pp. 143–160. Mathematical Science Publishers, Coventry, 2002.
[Kon93] Maxim, Kontsevich. Vassiliev's knot invariants. In I. M. Gelfand Seminar. Advances in Soviet Mathematics, Vol. 16, pp. 137–150. American Mathematical Society, Providence, RI, 1993.
[Kon99] Maxim, Kontsevich. Operads and motives in deformation quantization. Lett. Math. Phys., 48(1):35–72, 1999.
[Kos93] Antoni A., Kosinski. Differential manifolds. Pure and Applied Mathematics, Vol. 138. Academic Press, Boston, MA, 1993.
[Kos97] Ulrich, Koschorke. A generalization of Milnor's μ-invariants to higherdimensional link maps. Topology, 36(2):301–324, 1997.
[KR02] John R., Klein and John, Rognes. A chain rule in the calculus of homotopy functors. Geom. Topol., 6:853–887 (electronic), 2002.
[KS00] Maxim, Kontsevich and Yan, Soibelman. Deformations of algebras over operads and the Deligne conjecture. In Conférence Moshé Flato 1999, Vol. I (Dijon), Mathematical Physics Studies, Vol. 21, pp. 255–307. Kluwer Academic, Dordrecht, 2000.
[KSV97] J., Klein, R., Schwänzl, and R. M., Vogt. Comultiplication and suspension. Topology Appl., 77(1):1–18, 1997.
[KT06] Akira, Kono and Dai, Tamaki. Generalized cohomology. Translations of Mathematical Monographs, Vol. 230. American Mathematical Society, Providence, RI, 2006. Translated from the 2002 Japanese edition by Tamaki, Iwanami Series in Modern Mathematics.
[Kuh04] Nicholas J., Kuhn. Tate cohomology and periodic localization of polynomial functors. Invent. Math., 157(2):345–370, 2004.
[Kuh07] Nicholas J., Kuhn. Goodwillie towers and chromatic homotopy: an overview. In Proceedings of the Nishida Fest (Kinosaki 2003). Geometry and Topology Monographs, Vol. 10, pp. 245–279. Mathematical Science Publishers, Coventry, 2007.
[KW12] John, Klein and Bruce, Williams. Homotopical intersection theory, iii: Multirelative intersection problems. arXiv:1212.4420, 2012.
[Lee03] John M., Lee. Introduction to smooth manifolds. Graduate Texts in Mathematics, Vol. 218. Springer-Verlag, New York, 2003.
[LL06] José La, Luz. The Bousfield–Kan spectral sequence for Morava K-theory. Proc. Edinb. Math. Soc. (2), 49(3):683–699, 2006.
[LM12] Ayelet, Lindenstrauss and Randy, McCarthy. On the Taylor tower of relative K-theory. Geom. Topol., 16(2):685–750, 2012.
[LRV03] Wolfgang, Lück, Holger, Reich, and Marco, Varisco. Commuting homotopy limits and smash products. K-Theory, 30(2):137–165, 2003.
[LT09] Pascal, Lambrechts and Victor, Turchin. Homotopy graph-complex for configuration and knot spaces. Trans. Amer. Math. Soc., 361(1):207–222, 2009.
[LTV10] Pascal, Lambrechts, Victor, Turchin, and Ismar, Voli´c. The rational homology of spaces of long knots in codimension > 2. Geom. Topol., 14:2151–2187, 2010.
[Lur09] Jacob, Lurie. Higher topos theory. Annals of Mathematics Studies, Vol. 170. Princeton University Press, Princeton, NJ, 2009.
[LV14] Pascal, Lambrechts and Ismar, Voli´c. Formality of the little N-disks operad. Mem. Amer. Math. Soc., 230(1079):viii+116, 2014.
[Mac07] Tibor, Macko. The block structure spaces of real projective spaces and orthogonal calculus of functors. Trans. Amer. Math. Soc., 359(1):349–383 (electronic), 2007.
[Mat73] Michael, Mather. Hurewicz theorems for pairs and squares. Math. Scand., 32:269–272 (1974), 1973.
[Mat76] Michael, Mather. Pull-backs in homotopy theory. Canad. J. Math., 28(2):225–263, 1976.
[May72] J. P., May. The geometry of iterated loop spaces. Lecture Notes in Mathematics, Vol. 271. Springer-Verlag, Berlin, 1972.
[May90] J. P., May. Weak equivalences and quasifibrations. In Groups of selfequivalences and related topics (Montreal, PQ, 1988). Lecture Notes in Mathematics, Vol. 1425, pp. 91–101. Springer, Berlin, 1990.
[May92] J. Peter, May. Simplicial objects in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1992.
[May99] J. P., May. A concise course in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1999.
[McC01a] Rand, McCarthy. Dual calculus for functors to spectra. In Homotopy methods in algebraic topology (Boulder, CO, 1999). Contemporary Mathematics, Vol. 271, pp. 183–215. American Mathematical Society, Providence, RI, 2001.
[McC01b] John, McCleary. A user's guide to spectral sequences, Cambridge Studies in Advanced Mathematics, Vol. 58. Cambridge University Press, Cambridge, second edition, 2001.
[Mey90] Jean-Pierre, Meyer. Cosimplicial homotopies. Proc. Amer. Math. Soc., 108(1):9–17, 1990.
[Mil63] J., Milnor. Morse theory. Based on lecture notes by M., Spivak and R., Wells. Annals of Mathematics Studie, Vol. 51. Princeton University Press, Princeton, NJ, 1963.
[Mil84] Haynes, Miller. The Sullivan conjecture on maps from classifying spaces. Ann. Math. (2), 120(1):39–87, 1984.
[ML98] Saunders Mac, Lane. Categories for the working mathematician. Graduate Texts in Mathematics, Vol. 5. Springer-Verlag, New York, second edition, 1998.
[MO06] Andrew, Mauer-Oats. Algebraic Goodwillie calculus and a cotriple model for the remainder. Trans. Amer. Math. Soc., 358(5):1869–1895 (electronic), 2006.
[Moo53] John C., Moore. Some applications of homology theory to homotopy problems. Ann. Math. (2), 58:325–350, 1953.
[Mor12] Syunji, Moriya. Sinha's spectral sequence and homotopical algebra of operads. arXiv:1210.0996, 2012.
[MS02] James E., McClure and Jeffrey H., Smith. A solution of Deligne's Hochschild cohomology conjecture. In Recent progress in homotopy theory (Baltimore, MD, 2000). Contemporary Mathematics, Vol. 293, pp. 153–193. American Mathematical Society, Providence, RI, 2002.
[MS04a] James E., McClure and Jeffrey H., Smith. Cosimplicial objects and little n-cubes. I. Amer. J. Math., 126(5):1109–1153, 2004.
[MS04b] James E., McClure and Jeffrey H., Smith. Operads and cosimplicial objects: an introduction. In Axiomatic, enriched and motivic homotopy theory. NATO Science Series II Mathematics, Physics and Chemistry, Vol. 131, pp. 133–171. Kluwer Academic, Dordrecht, 2004.
[MSS02] Martin, Markl, Steve, Shnider, and Jim, Stasheff. Operads in algebra, topology and physics. Mathematical Surveys and Monographs, Vol. 96. American Mathematical Society, Providence, RI, 2002.
[MT68] Robert E., Mosher and Martin C., Tangora. Cohomology operations and applications in homotopy theory. Harper & Row, New York–London, 1968.
[Mun75] James R., Munkres. Topology: a first course. Prentice-Hall, Englewood Cliffs, NJ, 1975.
[Mun08] Brian A., Munson. A manifold calculus approach to link maps and the linking number. Algebr. Geom. Topol., 8(4):2323–2353, 2008.
[Mun10] Brian A., Munson. Introduction to the manifold calculus of Goodwillie– Weiss. Morfismos, 14(1):1–50, 2010.
[Mun11] Brian A., Munson. Derivatives of the identity and generalizations of Milnor's invariants. J. Topol., 4(2):383–405, 2011.
[Mun14] Brian A., Munson. A purely homotopy-theoretic proof of the Blakers– Massey theorem for n-cubes. Homology Homotopy Appl., 16(1):333–339, 2014.
[MV14] Brian A., Munson and Ismar, Volic. Cosimplicial models for spaces of links. J. Homotopy Relat. Struct., 9(2): 419–454, 2014.
[MW80] Michael, Mather and Marshall, Walker. Commuting homotopy limits and colimits. Math. Z., 175(1):77–80, 1980.
[MW09] Tibor, Macko and Michael, Weiss. The block structure spaces of real projective spaces and orthogonal calculus of functors. II. Forum Math., 21(6):1091–1136, 2009.
[Nam62] I., Namioka. Maps of pairs in homotopy theory. Proc. London Math. Soc. (3), 12:725–738, 1962.
[Nei10] Joseph, Neisendorfer. Algebraic methods in unstable homotopy theory. New Mathematical Monographs, Vol. 12. Cambridge University Press, Cambridge, 2010.
[NM78] Joseph, Neisendorfer and Timothy, Miller. Formal and coformal spaces. Illinois J. Math., 22(4):565–580, 1978.
[Ogl13] Crichton, Ogle. On the homotopy type of A(ΣX). J. Pure Appl. Algebra, 217(11):2088–2107, 2013.
[Pel11] Kristine E., Pelatt. A geometric homology representative in the space of long knots. arXiv:1111.3910, 2011.
[Pod11] Semën S., Podkorytov. On the homology of mapping spaces. Cent. Eur. J. Math., 9(6):1232–1241, 2011.
[Pup58] Dieter, Puppe. Homotopiemengen und ihre induzierten Abbildungen. I. Math. Z., 69:299–344, 1958.
[Qui73] Daniel, Quillen. Higher algebraic K-theory. I. In Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972). Lecture Notes in Mathematics, Vol. 341, pp. 85–147. Springer, Berlin, 1973.
[Rec70] David L., Rector. Steenrod operations in the Eilenberg–Moore spectral sequence. Comment. Math. Helv., 45:540–552, 1970.
[Rez13] Charles, Rezk. A streamlined proof of Goodwillie's n-excisive approximation. Algebr. Geom. Topol., 13(2):1049–1051, 2013.
[Rog] John, Rognes. Lecture notes on algebraic k-theory. Available at http://folk.uio.no/rognes/kurs/mat9570v10/akt.pdf.
[Rom10] Ana, Romero. Computing the first stages of the Bousfield–Kan spectral sequence. Appl. Algebra Engrg. Comm. Comput., 21(3):227–248, 2010.
[Sak08] Keiichi, Sakai. Poisson structures on the homology of the space of knots. In Groups, homotopy and configuration spaces, Geometry and Topology Monographs, Vol. 13, pp. 463–482. Mathematical Science Publishers, Coventry, 2008.
[Sak11] Keiichi, Sakai. BV-structures on the homology of the framed long knot space. arXiv:1110.2358, 2011.
[Sal01] Paolo, Salvatore. Configuration spaces with summable labels. In Cohomological methods in homotopy theory (Bellaterra, 1998), Progress in Mathematics, Vol. 196, pp. 375–395. Birkhäuser, Basel, 2001.
[Sal06] Paolo, Salvatore. Knots, operads, and double loop spaces. Int. Math. Res. Not., pages Art. ID 13628, 22, 2006.
[Seg68] Graeme|Segal. Classifying spaces and spectral sequences. Inst. Hautes Études Sci. Publ. Math., (34):105–112, 1968.
[Sel97] Paul, Selick. Introduction to homotopy theory. Fields Institute Monographs, Vol. 9. American Mathematical Society, Providence, RI, 1997.
[Shi96] Brooke E., Shipley. Convergence of the homology spectral sequence of a cosimplicial space. Amer. J. Math., 118(1):179–207, 1996.
[Sin01] Dev P., Sinha. The geometry of the local cohomology filtration in equivariant bordism. Homology Homotopy Appl., 3(2):385–406, 2001.
[Sin04] Dev P., Sinha. Manifold-theoretic compactifications of configuration spaces. Selecta Math. (NS), 10(3):391–428, 2004.
[Sin06] Dev P., Sinha. Operads and knot spaces. J. Amer. Math. Soc., 19(2):461– 486 (electronic), 2006.
[Sin09] Dev P., Sinha. The topology of spaces of knots: cosimplicial models. Amer. J. Math., 131(4):945–980, 2009.
[Sma59] Stephen, Smale. The classification of immersions of spheres in Euclidean spaces. Ann. Math. (2), 69:327–344, 1959.
[Smi02] V. A., Smirnov. A∞-structures and differentials of the Adams spectral sequence. Izv. Ross. Akad. Nauk Ser. Mat., 66(5):193–224, 2002.
[Spa67] E., Spanier. The homotopy excision theorem. Michigan Math. J., 14:245– 255, 1967.
[Spe71] C., Spencer. The Hilton–Milnor theorem and Whitehead products. J. London Math. Soc., 2(4):291–303, 1971.
[SS02] Kevin P., Scannell and Dev P., Sinha. A one-dimensional embedding complex. J. Pure Appl. Algebra, 170(1):93–107, 2002.
[ST14] Paul Arnaud, Songhafouo-Tsopméné. Formality of Sinha's cosimplicial model for long knots spaces. arXiv:1210.2561, 2014.
[Sta63] James Dillon, Stasheff. Homotopy associativity of H-spaces. I, II. Trans. Amer. Math. Soc. 108, 275–292; 108:293–312, 1963.
[Sta68] James D., Stasheff. Associated fibre spaces. Michigan Math. J., 15:457–470, 1968.
[Str66] Arne, Strøm. Note on cofibrations. Math. Scand., 19:11–14, 1966.
[Str68] Arne, Strøm. Note on cofibrations. II. Math. Scand., 22:130–142 (1969), 1968.
[Tam03] Dmitry E., Tamarkin. Formality of chain operad of little discs. Lett. Math. Phys., 66(1–2):65–72, 2003.
[tD08] Tammo tom, Dieck. Algebraic topology. EMS Textbooks in Mathematics. European Mathematical Society (EMS), Zürich, 2008.
[tDKP70] Tammo tom, Dieck, Klaus Heiner, Kamps, and Dieter, Puppe. Homotopietheorie. Lecture Notes in Mathematics, Vol. 157. Springer-Verlag, Berlin, 1970.
[Tho79] R.W., Thomason. Homotopy colimits in the category of small categories. Math. Proc. Cambridge Phil. Soc., 85(1):91–109, 1979.
[TT04] Victor, Turchin (Tourtchine). On the homology of the spaces of long knots. In Advances in topological quantum field theory. NATO Science Series II Mathematics, Physics and Chemistry, Vol. 179, pp. 23–52. Kluwer Academic, Dordrecht, 2004.
[TT06] Victor, Turchin (Tourtchine). What is one-term relation for higher homology of long knots. Mosc. Math. J., 6(1):169–194, 223, 2006.
[TT07] Victor, Turchin (Tourtchine). On the other side of the bialgebra of chord diagrams. J. Knot Theory Ramifications, 16(5):575–629, 2007.
[TT10] Victor, Turchin (Tourtchine). Hodge-type decomposition in the homology of long knots. J. Topol., 3(3):487–534, 2010.
[TT14] Victor, Turchin (Tourtchine). Delooping totalization of a multiplicative operad. J. Homotopy Relat. Struct., 9(2):349–418, 2014.
[Tur98] JamesM., Turner. Operations and spectral sequences. I. Trans. Amer.Math. Soc., 350(9):3815–3835, 1998.
[Vas90] V. A., Vassiliev. Cohomology of knot spaces. In Theory of singularities and its applications. Advances in Soviet Mathematics, Vol. 1, pp. 23–69. Amer. Math. Soc., Providence, RI, 1990.
[Vas99] V. A., Vassiliev. Homology of i-connected graphs and invariants of knots, plane arrangements, etc. In The Arnoldfest (Toronto, ON, 1997). Fields Institute Communications, Vol. 24, pp. 451–469. American Mathematical Society, Providence, RI, 1999.
[Vog73] Rainer M., Vogt. Homotopy limits and colimits. Math. Z., 134:11–52, 1973.
[Vog77] Rainer M., Vogt. Commuting homotopy limits. Math. Z., 153(1):59–82, 1977.
[Vol06a] Ismar, Volic. Configuration space integrals and Taylor towers for spaces of knots. Topology Appl., 153(15):2893–2904, 2006.
[Vol06b] Ismar, Volic. Finite type knot invariants and the calculus of functors. Compos. Math., 142(1):222–250, 2006.
[Wei94] Charles A., Weibel. An introduction to homological algebra. Cambridge Studies in Advanced Mathematics, Vol. 38. Cambridge University Press, Cambridge, 1994.
[Wei95] Michael, Weiss. Orthogonal calculus. Trans. Amer. Math. Soc., 347(10):3743–3796, 1995.
[Wei99] Michael, Weiss. Embeddings from the point of view of immersion theory I. Geom. Topol., 3:67–101 (electronic), 1999.
[Wei04] Michael S., Weiss. Homology of spaces of smooth embeddings. Q. J. Math., 55(4):499–504, 2004.
[Whi78] George W., Whitehead. Elements of homotopy theory. Graduate Texts in Mathematics, Vol. 61. Springer-Verlag, New York, 1978.
[Wit95] P. J., Witbooi. Adjunction of n-equivalences and triad connectivity. Publ. Mat., 39(2):367–377, 1995.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.