Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-18T00:12:02.525Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  19 August 2023

Vladimir Dotsenko
Affiliation:
Université de Strasbourg
Sergey Shadrin
Affiliation:
Universiteit van Amsterdam
Bruno Vallette
Affiliation:
Université Sorbonne Paris Nord
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Maurer–Cartan Methods in Deformation Theory
The Twisting Procedure
, pp. 166 - 174
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Agračev, A. A., and Gamkrelidze, R. V. 1980. Chronological algebras and non-stationary vector fields. Pages 135176, 243 of: Problems in geometry, Vol. 11 (Russian). Moscow: Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii.Google Scholar
[2]Armstrong, J., and Clarke, P. 2015. Curved A-infinity-categories: adjunction and homotopy. ArXiv e-prints. Available from the webpage: https://arxiv.org/abs/1506.03711.Google Scholar
[3]Arnol’d, V. I. 1965. Sur une propriété topologique des applications golbalement canoniques de la mécanique classique. C. R. Acad. Sci., Paris, 261, 37193722.Google Scholar
[4]Atiyah, M. F., and Bott, R. 1983. The Yang-Mills equations over Riemann surfaces. Philos. Trans. R. Soc. Lond., Ser. A, 308, 523615.Google Scholar
[5]Audin, M. 2004. Torus actions on symplectic manifolds. 2nd revised ed. edn. Prog. Math., vol. 93. Basel: Birkhäuser.Google Scholar
[6]Baker, H. F. 1905. Alternants and continuous groups. Proc. London Math. Soc., 3(2), 2447.Google Scholar
[7]Bandiera, R. 2014. Higher Deligne groupoids, derived brackets and deformation problems in holomorphic Poisson geometry. Ph.D. thesis, Università degli studi di Roma ‘La Sapienza’. Available from the webpage: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.702.2298&rep=rep1&type=pdf (September 2022).Google Scholar
[8]Batalin, I. A., and Vilkovisky, G. A. 1981. Gauge algebra and quantization. Phys. Lett. B, 102(1), 2731.CrossRefGoogle Scholar
[9]Batanin, M., and Markl, M. 2014. Crossed interval groups and operations on the Hochschild cohomology. J. Noncommut. Geom., 8(3), 655693.Google Scholar
[10]Baues, O. 1999. Left-symmetric algebras for gl(n). Trans. Amer. Math. Soc., 351(7), 29792996.Google Scholar
[11]Berger, C., and Fresse, B. 2004. Combinatorial operad actions on cochains. Math. Proc. Cambridge Philos. Soc., 137(1), 135174.CrossRefGoogle Scholar
[12]Berglund, A. 2015. Rational homotopy theory of mapping spaces via Lie theory for L-algebras. Homology Homotopy Appl., 17(2), 343369.CrossRefGoogle Scholar
[13]Bonfiglioli, A., and Fulci, R. 2011. Topics in noncommutative algebra: the theorem of Campbell, Baker, Hausdorff and Dynkin. Lecture Notes in Mathematics, vol. 2034. Berlin: Springer.Google Scholar
[14]Bourbaki, N. 1961. Éléments de mathématique. Fascicule XXVIII. Algèbre commutative. Chapitre 3: Graduations, filtrations et topologies. Chapitre 4: Idéaux premiers associés et décomposition primaire. Actualités Scientifiques et Industrielles, No. 1293. Paris: Hermann.Google Scholar
[15]Bousfield, A. K., and Guggenheim, V. K. A. M. 1976. On PL de Rham theory and rational homotopy theory. Memoirs of the AMS, 8.Google Scholar
[16]Brown, , Jr., E.H. 1959. Twisted tensor products. I. Ann. Math., 69(2), 223246.Google Scholar
[17]Buijs, U., Félix, Y., and Murillo, A. 2011. L models of based mapping spaces. J. Math. Soc. Japan, 63(2), 503524.Google Scholar
[18]Buijs, U., Félix, Y., Murillo, A., and Tanré, D. 2020. Lie models in topology. Prog. Math., vol. 335. Cham: Birkhäuser.Google Scholar
[19]Calderbank, D. M. J., and Diemer, T. 2001. Differential invariants and curved Bernstein-Gelfand-Gelfand sequences. J. Reine Angew. Math., 537, 67103.Google Scholar
[20]Campbell, J. E. 1896/97. On a law of combination of operators bearing on the theory of continuous transformation groups. Proc. Lond. Math. Soc., 28, 381390.Google Scholar
[21]Campbell, J. E. 1897/98. On a law of combination of operators (second paper). Proc. Lond. Math. Soc., 29, 1432.Google Scholar
[22]Cartan, É. 1904. Sur la structure des groupes infinis de transformation. Ann. Sci. École Norm. Sup., 21(3), 153206.Google Scholar
[23]Cartan, H. 1955. Séminaire Henri Cartan, Tome 7 (1954–1955). 2(7). Available from the webpage: www.numdam.org/volume/SHC_1954-1955_7_1/.Google Scholar
[24]Chan, M., Galatius, S., and Payne, S. 2021. Tropical curves, graph complexes, and top weight cohomology of g. J. Am. Math. Soc., 34(2), 565594.CrossRefGoogle Scholar
[25]Chapoton, F., and Livernet, M. 2001. Pre-Lie algebras and the rooted trees operad. Internat. Math. Res. Notices, 8, 395408.CrossRefGoogle Scholar
[26]Chen, K.-T. 1973. Iterated integrals of differential forms and loop space homology. Ann. Math., 97(2), 217246.Google Scholar
[27]Chen, K.-T. 1977. Iterated path integrals. Bull. Am. Math. Soc., 83, 831879.Google Scholar
[28]Chuang, J., and Lazarev, A. 2013. Combinatorics and formal geometry of the Maurer-Cartan equation. Lett. Math. Phys., 103(1), 79112.CrossRefGoogle Scholar
[29]Church, T., Ellenberg, J. S., and Farb, B. 2015. FI-modules and stability for representations of symmetric groups. Duke Math. J., 164(9), 18331910.Google Scholar
[30]Cohen, F. R. 1976. The homology of n+1-spaces. Pages vii+490 of: The homology of iterated loop spaces (Cohen, Frederick R. and Lada, Thomas J. and May, J. Peter). Lecture Notes in Mathematics, Vol. 533. Berlin: Springer-Verlag.Google Scholar
[31]Căldăraru, A., and Tu, J. 2013. Curved A algebras and Landau-Ginzburg models. New York J. Math., 19, 305342.Google Scholar
[32]Deligne, P. Letter to Millson, April 24, 1986. Available from the webpage: http://publications.ias.edu/sites/default/files/millson.pdf.Google Scholar
[33]Deligne, P. 1974. Théorie de Hodge. III. Inst. Hautes Études Sci. Publ. Math., 44, 577.Google Scholar
[34]Dolgushev, V., and Willwacher, T. 2015. Operadic twisting – with an application to Deligne’s conjecture. J. Pure Appl. Algebra, 219(5), 13491428.Google Scholar
[35]Dolgushev, V. A., and Rogers, C. L. 2012. Notes on algebraic operads, graph complexes, and Willwacher’s construction. Pages 25145 of: Mathematical aspects of quantization. Contemp. Math., vol. 583. Providence, RI: American Mathematical Society.Google Scholar
[36]Dolgushev, V. A., and Rogers, C. L. 2015. A version of the Goldman-Millson theorem for filtered L-algebras. J. Algebra, 430, 260302.Google Scholar
[37]Dolgushev, V. A., and Rogers, C. L. 2017. On an enhancement of the category of shifted L-algebras. Appl. Categ. Structures, 25(4), 489503.Google Scholar
[38]Dolgushev, V. A., Hoffnung, A. E., and Rogers, C. L. 2015. What do homotopy algebras form? Adv. Math., 274, 562605.CrossRefGoogle Scholar
[39]Donaldson, S. K. 1983. An application of gauge theory to four dimensional topology. J. Differ. Geom., 18, 279315.Google Scholar
[40]Donaldson, S. K., and Kronheimer, P. B. 1997. The geometry of four-manifolds. Paperback ed. edn. Oxford Math. Monogr. Oxford: Clarendon Press.Google Scholar
[41]Dotsenko, V., and Khoroshkin, A. 2020. Homotopical rigidity of the pre-Lie operad. ArXiv e-prints. Available from the webpage: https://arxiv.org/abs/2002.12918.Google Scholar
[42]Dotsenko, V., Shadrin, S., and Vallette, B. 2013. Givental group action on topological field theories and homotopy Batalin–Vilkovisky algebras. Adv. Math., 236, 224256.Google Scholar
[43]Dotsenko, V., Shadrin, S., and Vallette, B. 2015a. De Rham cohomology and homotopy Frobenius manifolds. J. Eur. Math. Soc. (JEMS), 17(3), 535547.Google Scholar
[44]Dotsenko, V., Shadrin, S., and Vallette, B. 2015b. Givental action and trivialisation of circle action. J. Éc. polytech. Math., 2, 213246.Google Scholar
[45]Dotsenko, V., Shadrin, S., and Vallette, B. 2016. Pre-Lie deformation theory. Mosc. Math. J., 16(3), 505543.CrossRefGoogle Scholar
[46]Dotsenko, V., Shadrin, S., and Vallette, B. 2019. Toric varieties of Loday’s associahedra and noncommutative cohomological field theories. J. Topol., 12(2), 463535.Google Scholar
[47]Dotsenko, V., Shadrin, S., Vaintrob, A., and Vallette, B. 2022. Deformation theory of cohomological field theories. arXiv e-prints. Available from the webpage: https://arxiv.org/abs/2006.01649.Google Scholar
[48]Drinfeld, V. 2014. A letter from Kharkov to Moscow. EMS Surv. Math. Sci., 1(2), 241248. Translated from the Russian by Keith Conrad.Google Scholar
[49]Dupont, J. L. 1976. Simplicial de Rham cohomology and characteristic classes of flat bundles. Topology, 15(3), 233245.CrossRefGoogle Scholar
[50]Dynkin, E. B. 1947. Calculation of the coefficients in the Campbell-Hausdorff formula. Doklady Akad. Nauk SSSR (N.S.), 57, 323326.Google Scholar
[51]Floer, A. 1988. Morse theory for Lagrangian intersections. J. Differ. Geom., 28(3), 513547.Google Scholar
[52]Fresse, B. 2017a. Homotopy of operads and Grothendieck-Teichmüller groups. Part 1. Mathematical Surveys and Monographs, vol. 217. The algebraic theory and its topological background. Providence, RI: American Mathematical Society.Google Scholar
[53]Fresse, B. 2017b. Homotopy of operads and Grothendieck-Teichmüller groups. Part 2. Mathematical Surveys and Monographs, vol. 217. The applications of (rational) homotopy theory methods. Providence, RI: American Mathematical Society.Google Scholar
[54]Fresse, B., Turchin, V., and Willwacher, T. 2020. On the rational homotopy type of embedding spaces of manifolds in Rn. arXiv e-prints. Available from the webpage: https://arxiv.org/abs/2008.08146.Google Scholar
[55]Frölicher, A., and Nijenhuis, A. 1957. A theorem on stability of complex structures. Proc. Nat. Acad. Sci. U.S.A., 43, 239241.Google Scholar
[56]Fukaya, K., Oh, Y.-G., Ohta, H., and Ono, K. 2009a. Lagrangian intersection Floer theory: anomaly and obstruction. Part I. AMS/IP Studies in Advanced Mathematics, vol. 46. Providence, RI: American Mathematical Society.Google Scholar
[57]Fukaya, K., Oh, Y.-G., Ohta, H., and Ono, K. 2009b. Lagrangian intersection Floer theory: anomaly and obstruction. Part II. AMS/IP Studies in Advanced Mathematics, vol. 46. Providence, RI: American Mathematical Society.Google Scholar
[58]Galvez-Carrillo, I., Tonks, A., and Vallette, B. 2012. Homotopy Batalin– Vilkovisky algebras. J. Noncommut. Geom., 6(3), 539602.Google Scholar
[59]Gerstenhaber, M. 1963. The cohomology structure of an associative ring. Ann. Math. (2), 78, 267288.Google Scholar
[60]Gerstenhaber, M. 1964. On the deformation of rings and algebras. Ann. Math. (2), 79, 59103.Google Scholar
[61]Gerstenhaber, M., and Voronov, A. A. 1995. Homotopy G-algebras and moduli space operad. Internat. Math. Res. Notices, 141153.Google Scholar
[62]Getzler, E. 2009. Lie theory for nilpotent L-algebras. Ann. Math. (2), 170(1), 271301.Google Scholar
[63]Ginzburg, V., and Kapranov, M. 1994. Koszul duality for operads. Duke Math. J., 76(1), 203272.Google Scholar
[64]Ginzburg, V., and Kapranov, M. 1995. Erratum to: ‘Koszul duality for operads’. Duke Math. J., 80(1), 293.Google Scholar
[65]Goldman, W. M., and Millson, J. J. 1988. The deformation theory of representations of fundamental groups of compact Kähler manifolds. Inst. Hautes Études Sci. Publ. Math., 4396.Google Scholar
[66]Hain, R. M. 1984. Iterated integrals and homotopy periods. Mem. Am. Math. Soc., vol. 291.Google Scholar
[67]Hamilton, M. J. D. 2017. Mathematical gauge theory. With applications to the standard model of particle physics. Universitext. Springer.Google Scholar
[68]Hausdorff, F. 1906. Die symbolische Exponentialformel in der Gruppentheorie. Leipz. Ber. 58, 19-48 (1906).Google Scholar
[69]Henriques, André. 2008. Integrating L-algebras. Compos. Math., 144(4), 1017– 1045.Google Scholar
[70]Hilton, P. J. 1955. On the homotopy groups of the union of spheres. J. London Math. Soc., 30, 154172.Google Scholar
[71]Hinich, V. 1997. Descent of Deligne groupoids. Internat. Math. Res. Notices, 223239.Google Scholar
[72]Hinich, V. 2001. DG coalgebras as formal stacks. J. Pure Appl. Algebra, 162(2-3), 209250.Google Scholar
[73]Hirsh, J., and Millès, J. 2012. Curved Koszul duality theory. Math. Ann., 354(4), 14651520.Google Scholar
[74]Hoffbeck, E., Leray, J., and Vallette, B. 2020. Properadic homotopical calculus. Int. Math. Res. Not., rnaa091.Google Scholar
[75]Husemoller, D., Moore, J. C., and Stasheff, J. 1974. Differential homological algebra and homogeneous spaces. J. Pure Appl. Algebra, 5, 113185.Google Scholar
[76]Kadeišvili, T. V. 1980. On the theory of homology of fiber spaces. Uspekhi Mat. Nauk, 35(3(213)), 183188. International Topology Conference (Moscow State Univ., Moscow, 1979).Google Scholar
[77]Khoroshkin, A., and Willwacher, T. 2019. Real moduli space of stable rational curves revisited. arXiv e-prints. Available from the webpage: https://arxiv.org/abs/1905.04499.Google Scholar
[78]Klein, F. 1893. Vergleichende Betrachtungen Forschungen. Math. Ann., 43(1), 63100. über neuere geometrischeGoogle Scholar
[79]Kobayashi, S., and Nomizu, K. 1963. Foundations of differential geometry. I. Intersci. Tracts Pure Appl. Math., vol. 15. New York, NY: Interscience Publishers.Google Scholar
[80]Kodaira, K., and Spencer, D. C. 1958a. On deformations of complex analytic structures. I. Ann. Math. (2), 67, 328401.CrossRefGoogle Scholar
[81]Kodaira, K., and Spencer, D. C. 1958b. On deformations of complex analytic structures. II. Ann. Math. (2), 67, 403466.Google Scholar
[82]Kodaira, K., Nirenberg, L., and Spencer, D. C. 1958. On the existence of deformations of complex analytic structures. Ann. Math. (2), 68, 450459.Google Scholar
[83]Kontsevich, M. 1993a. Formal (non)commutative symplectic geometry. Pages 173–187 of: The Gel’fand Mathematical Seminars, 19901992. Boston, MA: Birkhäuser Boston.Google Scholar
[84]Kontsevich, M. 1993b. Formal (non)commutative symplectic geometry. Pages 173–187 of: The Gel’fand Mathematical Seminars, 19901992. Boston, MA: Birkhäuser Boston.Google Scholar
[85]Kontsevich, M. 1994. Feynman diagrams and low-dimensional topology. Pages 97–121 of: First European Congress of Mathematics, Vol. II (Paris, 1992). Progr. Math., vol. 120. Basel: Birkhäuser.Google Scholar
[86]Kontsevich, M. 1997. Formality conjecture. Pages 139–156 of: Deformation theory and symplectic geometry (Ascona, 1996). Math. Phys. Stud., vol. 20. Dordrecht: Kluwer Academic Publishers.Google Scholar
[87]Kontsevich, M. 1999. Operads and motives in deformation quantization. Lett. Math. Phys., 48(1), 3572. Moshé Flato (1937–1998).Google Scholar
[88]Kontsevich, M. 2003. Deformation quantization of Poisson manifolds. Lett. Math. Phys., 66(3), 157216.Google Scholar
[89]Kontsevich, M., and Soibelman, Y. 2000. Deformations of algebras over operads and the Deligne conjecture. Pages 255307 of: Conférence Moshé Flato 1999, Vol. I (Dijon). Math. Phys. Stud., vol. 21. Dordrecht: Kluwer Academic Publishers.Google Scholar
[90]Koszul, Jean-Louis. 1961. Domaines bornés homogènes et orbites de groupes de transformations affines. Bull. Soc. Math. France, 89, 515533.Google Scholar
[91]Kuranishi, M. 1962. On the locally complete families of complex analytic structures. Ann. Math. (2), 75, 536577.Google Scholar
[92]Lada, T., and Markl, M. 1995. Strongly homotopy Lie algebras. Comm. Algebra, 23(6), 21472161.Google Scholar
[93]Lambrechts, P., and Volić, I. 2014. Formality of the little N-disks operad. Mem. Amer. Math. Soc., 230(1079), viii+116.Google Scholar
[94]Lawrence, R., and Sullivan, D. 2014. A formula for topology/deformations and its significance. Fund. Math., 225, 229242.Google Scholar
[95]Lazard, M. 1954. Sur les groupes nilpotents et les anneaux de Lie. Ann. Sci. Ecole Norm. Sup. (3), 71, 101190.CrossRefGoogle Scholar
[96]Lazarev, A. 2013. Maurer-Cartan moduli and models for function spaces. Adv. Math., 235, 296320.Google Scholar
[97]Loday, J.-L., and Vallette, B. 2012. Algebraic operads. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 346. Berlin: Springer-Verlag.Google Scholar
[98]Lurie, J. 2010. Moduli problems for ring spectra. Pages 10991125 of: Proceedings of the International Congress of Mathematicians. Volume II. New Delhi: Hindustan Book Agency.Google Scholar
[99]Mal’cev, A. I. 1949. Nilpotent torsion-free groups. Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 13, 201212.Google Scholar
[100]Manchon, D. 2011. A short survey on pre-Lie algebras. Pages 89102 of: Noncommutative geometry and physics: renormalisation, motives, index theory. ESI Lectures in Mathematics and Physics. Zürich: European Mathematical Society.Google Scholar
[101]Manchon, D., and Saïdi, A. 2011. Lois pré-Lie en interaction. Comm. Algebra, 39(10), 36623680.Google Scholar
[102]Manetti, M. 2022. Lie methods in deformation theory. Springer Monogr. Math.Google Scholar
[103]Manin, Y. I. 1997. Gauge field theory and complex geometry. Transl. from the Russian by N. Koblitz and J. R. King. With an appendix by S. Merkulov. 2nd ed. edn. Grundlehren Math. Wiss., vol. 289. Berlin: Springer.Google Scholar
[104]Markl, M. 2007a. Cohomology operations and the Deligne conjecture. Czechoslovak Math. J., 57(132)(1), 473503.Google Scholar
[105]Markl, M. 2007b. Lie elements in pre-Lie algebras, trees and cohomology operations. J. Lie Theory, 17(2), 241261.Google Scholar
[106]Markl, M. 2012. Deformation theory of algebras and their diagrams. CBMS Regional Conference Series in Mathematics, vol. 116. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI.Google Scholar
[107]Markl, M. 2015. On the origin of higher braces and higher-order derivations. J. Homotopy Relat. Struct., 10(3), 637667.Google Scholar
[108]Maurer, L. 1888. Über allgemeinere Invarianten-Systeme. Münch. Ber. 103150.Google Scholar
[109]May, J. P., and Ponto, K. 2012. More concise algebraic topology. Localization, completion, and model categories. Chicago, IL: University of Chicago Press.Google Scholar
[110]May, J. P. 1972. The geometry of iterated loop spaces. Lectures Notes in Mathematics, Vol. 271. Berlin: Springer-Verlag.Google Scholar
[111]McClure, J. E., and Smith, J. H. 2002. A solution of Deligne’s Hochschild cohomology conjecture. Pages 153193 of: Recent progress in homotopy theory (Baltimore, MD, 2000). Contemp. Math., vol. 293. Providence, RI: American Mathematical Society.Google Scholar
[112]Merkulov, S. 2022. Twisting of properads. arXiv e-prints. Available from the webpage: https://arxiv.org/abs/2209.06742.Google Scholar
[113]Merkulov, S., and Vallette, B. 2009a. Deformation theory of representations of prop(erad)s. I. J. Reine Angew. Math., 634, 51106.Google Scholar
[114]Merkulov, S., and Vallette, B. 2009b. Deformation theory of representations of prop(erad)s. II. J. Reine Angew. Math., 636, 123174.Google Scholar
[115]Merkulov, S., and Willwacher, T. 2015. Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves. arXiv e-prints. Available from the webpage: https://arxiv.org/abs/1511.07808.Google Scholar
[116]Milnor, J. W., and Stasheff, J. D. 1974. Characteristic classes. Ann. Math. Stud., vol. 76. Princeton, NJ: Princeton University Press.Google Scholar
[117]Morgan, J. W. 1998. An introduction to gauge theory. Pages 53143 of: Gauge theory and the topology of four-manifolds. Lectures of the graduate summer school. Providence, RI: American Mathematical Society.Google Scholar
[118]Naber, G. L. 2011a. Topology, geometry and gauge fields. Foundations. 2nd ed. edn. Texts Appl. Math., vol. 25. Berlin: Springer.Google Scholar
[119]Naber, G. L. 2011b. Topology, geometry, and gauge fields. Interactions. 2nd ed. edn. Appl. Math. Sci., vol. 141. New York, NY: Springer.Google Scholar
[120]Neisendorfer, J. 1978. Lie algebras, coalgebras and rational homotopy theory for nilpotent spaces. Pac. J. Math., 74, 429460.Google Scholar
[121]Nijenhuis, A. 1955. Jacobi-type identities for bilinear differential concomitants of certain tensor fields. I, II. Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indag. Math., 17, 390–397, 398403.Google Scholar
[122]Nijenhuis, A., and Richardson, Jr., R. W. 1964. Cohomology and deformations of algebraic structures. Bull. Amer. Math. Soc., 70, 406411.Google Scholar
[123]Nijenhuis, A., and Richardson, Jr., R. W. 1966. Cohomology and deformations in graded Lie algebras. Bull. Amer. Math. Soc., 72, 129.Google Scholar
[124]Oudom, J.-M., and Guin, D. 2008. On the Lie enveloping algebra of a pre-Lie algebra. J. K-Theory, 2(1), 147167.Google Scholar
[125]Palamodov, V. P. 1976. Deformations of complex spaces. Uspehi Mat. Nauk, 31(3), 129194.Google Scholar
[126]Positselski, L. 2011. Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence. Mem. Amer. Math. Soc., 212(996), vi+133.Google Scholar
[127]Positselski, L. 2018. Weakly curved A-algebras over a topological local ring. Mém. Soc. Math. Fr. (N.S.), vi+206.Google Scholar
[128]Pridham, J. P. 2010. Unifying derived deformation theories. Adv. Math., 224(3), 772826.Google Scholar
[129]Quillen, D. 1969. Rational homotopy theory. Ann. Math. (2), 90, 205295.Google Scholar
[130]Robert-Nicoud, D. 2018. Deformation theory with homotopy algebra structures on tensor products. Doc. Math., 189240.Google Scholar
[131]Robert-Nicoud, D. 2019. Representing the deformation ∞-groupoid. Algebr. Geom. Topol., 19(3), 14531476.Google Scholar
[132]Robert-Nicoud, D., and Vallette, B. 2020. Higher Lie theory. arXiv e-prints. Available from the webpage: https://arxiv.org/abs/2010.10485.Google Scholar
[133]Robert-Nicoud, D., and Wierstra, F. 2019. Homotopy morphisms between convolution homotopy Lie algebras. J. Noncommut. Geom., 13(4), 14631520.Google Scholar
[134]Roca Lucio, V. 2022. The integration theory of curved absolute homotopy Lie algebras. arXiv e-prints. Available from the webpage: https://arxiv.org/abs/2207.11115.Google Scholar
[135]Schlessinger, M., and Stasheff, J. 2012. Deformation theory and rational homotopy type. ArXiv e-prints. Available from the webpage: https://arxiv.org/abs/1211.1647.Google Scholar
[136]Schouten, J. A. 1940. Ueber Differentialkomitanten zweier kontravarianter Grössen. Nederl. Akad. Wetensch., Proc., 43, 449452.Google Scholar
[137]Schouten, J. A. 1954. On the differential operators of first order in tensor calculus. Pages 17 of: Convegno Internazionale di Geometria Differenziale, Italia, 1953. Roma: Edizioni Cremonese.Google Scholar
[138]Segal, D. 1992. The structure of complete left-symmetric algebras. Math. Ann., 293(3), 569578.Google Scholar
[139]Stasheff, J. 1963. Homotopy associativity of H-spaces. I, II. Trans. Amer. Math. Soc. 108 (1963), 275-292; ibid., 108, 293312.Google Scholar
[140]Sullivan, D. 1977. Infinitesimal computations in topology. Inst. Hautes Études Sci. Publ. Math., 269331 (1978).Google Scholar
[141]Tamarkin, D. 2007. What do dg-categories form? Compos. Math., 143(5).Google Scholar
[142]Tamarkin, D. E. 2003. Formality of chain operad of little discs. Lett. Math. Phys., 66(1–2), 6572.Google Scholar
[143]Toën, B. 2017. Problèmes de modules formels. Astérisque, Exp. No. 1111, 199244. Séminaire Bourbaki. Vol. 2015/2016. Exposés 11041119.Google Scholar
[144]Tu, L. W. 2017. Differential geometry. Connections, curvature, and characteristic classes. Grad. Texts Math., vol. 275. Springer.Google Scholar
[145]Turchin, V., and Willwacher, T. 2017. Commutative hairy graphs and representations of Out(Fr). J. Topol., 10(2), 386411.CrossRefGoogle Scholar
[146]Uehara, H., and Massey, W. S. 1957. The Jacobi identity for Whitehead products. Pages 361377 of: Algebraic geometry and topology. A symposium in honor of S. Lefschetz. Princeton, N.J: Princeton University Press.Google Scholar
[147]Vallette, B. 2008. Manin products, Koszul duality, Loday algebras and Deligne conjecture. J. Reine Angew. Math., 620, 105164.Google Scholar
[148]Vinberg, È. B. 1963. The theory of homogeneous convex cones. Trudy Moskov. Mat. Obšč., 12, 303358.Google Scholar
[149]Voronov, A. A., and Gerstenkhaber, M. 1995. Higher-order operations on the Hochschild complex. Funktsional. Anal. i Prilozhen., 29(1), 16, 96.Google Scholar
[150]Warner, F. W. 1983. Foundations of differentiable manifolds and Lie groups. Reprint. Vol. 94. New York, NY: Springer.Google Scholar
[151]Whitehead, G. W. 1946. On products in homotopy groups. Ann. Math (2), 47, 460475.Google Scholar
[152]Whitehead, J. H. C. 1941. On adding relations to homotopy groups. Ann. Math. (2), 42, 409428.Google Scholar
[153]Wierstra, F. 2019. Algebraic Hopf invariants and rational models for mapping spaces. J. Homotopy Relat. Struct., 14(3), 719747.Google Scholar
[154]Willwacher, T. 2015. M. Kontsevich’s graph complex and the Grothendieck-Teichmüller Lie algebra. Invent. Math., 200(3), 671760.CrossRefGoogle Scholar
[155]Willwacher, T. 2022. Pre-Lie pairs and triviality of the Lie bracket on the twisted hairy graph complexes. Int. Math. Res. Not., 2022(23), 1820518255.Google Scholar
[156]Zwiebach, B. 1993. Closed string field theory: quantum action and the Batalin– Vilkovisky master equation. Nuclear Physics B, 390(1), 33152.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Vladimir Dotsenko, Université de Strasbourg, Sergey Shadrin, Universiteit van Amsterdam, Bruno Vallette, Université Sorbonne Paris Nord
  • Book: Maurer–Cartan Methods in Deformation Theory
  • Online publication: 19 August 2023
  • Chapter DOI: https://doi.org/10.1017/9781108963800.009
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Vladimir Dotsenko, Université de Strasbourg, Sergey Shadrin, Universiteit van Amsterdam, Bruno Vallette, Université Sorbonne Paris Nord
  • Book: Maurer–Cartan Methods in Deformation Theory
  • Online publication: 19 August 2023
  • Chapter DOI: https://doi.org/10.1017/9781108963800.009
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Vladimir Dotsenko, Université de Strasbourg, Sergey Shadrin, Universiteit van Amsterdam, Bruno Vallette, Université Sorbonne Paris Nord
  • Book: Maurer–Cartan Methods in Deformation Theory
  • Online publication: 19 August 2023
  • Chapter DOI: https://doi.org/10.1017/9781108963800.009
Available formats
×