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Advances in Two-Dimensional Homotopy and Combinatorial Group Theory
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    Advances in Two-Dimensional Homotopy and Combinatorial Group Theory
    • Online ISBN: 9781316555798
    • Book DOI: https://doi.org/10.1017/9781316555798
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Book description

This volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a quarter of a century ago in the volume Two-dimensional Homotopy and Combinatorial Group Theory (LMS 197), the editors here bring together much remarkable progress that has been obtained in the intervening years. And while the fundamental open questions, such as the Andrews–Curtis Conjecture and the Whitehead asphericity problem remain to be (fully) solved, this book will provide both students and experts with an overview of the state of the art and work in progress. Ample references are included to the LMS 197 volume, as well as a comprehensive bibliography bringing matters entirely up to date.

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Contents

References
[I] Hog-Angeloni, C., Metzler, W., and Sieradski, A. (eds). 1993. Two dimensional Homotopy and Combinatorial Group Theory. London Math. Soc. Lecture Note Series 197, Cambridge University Press.
[AKN09] A. K., Naimzada, S., Stefani, A., Torriero. 2009. Networks, Topology and Dynamics. Theory and applications to economics and social systems edn. Springer-Verlag. [Chapter 5].
[Ans91] Anshel, I. L. 1991. A Freiheitssatz for a class of two-relator groups. Journal of Pure and Applied Algebra, 72, 207–250. [Chapter 7].
[Art81] Artamonov, V. A. 1981. Projective, nonfree modules over group rings of solvable groups. Math. USSR Sbornik., 116, 232–244. [Chapter 1].
[BaMi16] Barmak, J., and Minian, E. 2016. A new test for asphericity and diagrammatic reducibility of group presentations. preprint, arXiv:1601.00604. [Chapter 4].
[BaGr69] Barnett, D., and Gruenbaum, B. 1969. On Steinitz's theorem concerning convex 3-polytopes and on some properties of planar graphs. Many Facets of Graph Theory, Proc. Conf. Western Michigan Uni., Kalamazoo/Mi. 1968, 27–40.[Chapter 5].
[Bau74] Baumslag, G. 1974. Finitely presented metabelian groups. Proc. Second international Conference in Group Theory, Lecture Notes in Math., 372, 65–74. [Chapters 1, 6].
[BaSo62] Baumslag, G., and Solitar, S. 1962. Some two-generator one-relator non-Hopfian groups. Bull. Amer. Math. Soc., 68, 199–201. [Chapter 1].
[BeWe99] Becker, T., and Weispfenning, V. 1999. Groebner bases. A computational approach to commutative algebra. Graduate Texts in Math., vol. 141. Springer-Verlag, New York. [Chapter 5].
[Ber] Berge, J. SnapPea. [Chapter 5].
[Ber78] Bergman, G. M. 1978. The diamond lemma for ring theory. Adv. in Math., 29 (2), 178–218. [Chapter 5].
[BeHi08] Berrick, A., and Hillman, J. 2008. The Whitehead Conjecture and L(2)-Betti numbers. In: Chatterji, I. (ed), Guido's Book of Conjectures. Monographie No. 40 De L' Enseignement Mathematique. [Chapter 4].
[BeDu79] Berridge, P. H., and Dunwoody, M. J. 1979. Non-free projective modules for torsion-free groups. J. London Math. Soc., 19(2), 433–436. [Chapter 1].
[BeBr97] Bestvina, M., and Brady, N. 1997. Morse theory and finiteness properties of groups. Invent. Math., 129, 445–470. [Chapters 1, 4, 6, 7].
[BeLaWa97] Beyl, F. R., Latiolais, M. P., and Waller, N. 1997. Classification of 2-complexes whose finite fundamental group is that of a 3-manifold. Proc. Edinburgh Math. Soc., 40, 69–84. [Chapter 1].
[BeWa05] Beyl, F. R., and Waller, N. 2005. A stably-free nonfree module and its relevance for homotopy classification, case Q 28. Algebraic & Geometric Topology, 5, 899–910. [Chapter 1].
[BeWa08] Beyl, F. R., and Waller, N. 2008. Examples of exotic free 2-complexes and stably free nonfree modules for quaternion groups. Algebraic & Geometric Topology, 8, 1–17. [Chapter 1].
[BeWa13] Beyl, F. R., and Waller, N. 2013. The geometric realization problem for algebraic 2-complexes. Preliminary version, unpublished, [Chapter 1].
[Big93] Biggs, N. 1993. Algebraic Graph Theory. Cambridge mathematical library (2nd ed.) edn. Cambridge University Press. [Chapter 5].
[Bir13] Biroth, L. 2013. Heegaard-Diagramme der 3-Sphäre und die Andrews-Curtis-Vermutung. Masterthesis, Johannes Gutenberg University Mainz 2013 (unpublished). [Chapter 2].
[BiSt80] Bieri, R., and Strebel, R. 1980. Valuations and finitely presented metabelian groups. Proc. London Math. Soc. (3), 41, 439–464. [Chapters 1, 6].
[Bla10] Blaavand, Jakob. 2010. 3-manifolds derived from link invariants. lecture notes, University of California, Berkeley. [Chapter 3].
[BlTu06a] Blanchet, C., and Turaev, V. 2006a. Axiomatic approach to Topological Quantum Field theory. Elsevier Ltd. [Chapter 3].
[BlTu06b] Blanchet, C., and Turaev, V. 2006b. Quantum 3-Manifold Invariants. Elsevier Ltd. [Chapter 3].
[Bob00] Bobtcheva, Ivelina. 2000. On Quinn's Invariants of 2-dimensional CW-complexes. arXiv math. GT. [Chapter 3].
[BoQu05] Bobtcheva, Ivelina, and Quinn, Frank. 2005. The reduction of quantum invariants of 4-thickenings. Fund. Math., 188, 21–43. [Chapter 3].
[BoLuMy05] Borovik, A.V., Lubotzky, A., and Myasnikov, A.G. 2005. The finitary Andrews-Curtis conjecture. In: Infinite groups: geometric, combinatorial and dynamical aspects. Progr. Math., vol. 248, pp.15-30, Birkhauser, Basel. [Chapters 2, 3].
[Bri15] Bridson, M. 2015. The complexity of balanced presentations and the Andrews-Curtis conjecture. arXiv:1504.04187. [Chapter 2].
[BrTw07] Bridson, M., and Tweedale, M. 2007. Deficieny and abelianized deficiency of some virtually free groups. Math. Proc. Cambridge Phil. Soc., 143, 257–264. [Chapters 6, 7].
[BrTw08] Bridson, M. R., and Tweedale, M. 2008. Putative relation gaps. Guido's Book of Conjectures. Monographie No. 40 De L'Enseignement Math'ematique. [Chapter 1].
[BrTw14] Bridson, M. R., and Tweedale, M. 2014. Constructing presentations of subgroups of right-angled Artin groups. Geom. Dedicata, 169, 1– 14. [Chapters 1, 6].
[Bro87] Brown, K. S. 1987. Finiteness properties of groups. J. Pure Appl. Algebra, 44, 45–75. [Chapters 1, 6].
[Bro76] Browning, W.J. 1976. Normal generators of finite groups. manuscript. http://www.cambridge.org/9781316600900, [Chapter 2].
[Bur01] Burdon, M. 2001. Embedding 2-polyhedra with regular neighborhoods which have sphere boundaries. PhD thesis, Portland State University. [Chapter 5].
[CaEi56] Cartan, H., and Eilenberg, S. 1956. Homological algebra. Princeton Mathematical Series, vol. 19. Princeton, NJ: Princeton University Press. [Chapter 1].
[ChdW14] Christmann, M., and de Wolff, T. 2014. A sharp upper bound for the complexity of labeled oriented trees. preprint, arXiv:1412.7257. [Chapter 4].
[Coh64] Cohn, P. M. 1964. Free ideal rings. J. Algebra, 1, 47–69. [Chapter 1].
[CoGrKo74] Cossey, J., Gruenberg, K. W., and Kovacs, L. G. 1974. Presentation rank of a direct product of finite groups. J. Algebra, 28, 597–603. [Chapters 1, 6].
[Dun72] Dunwoody, M. J. 1972. Relation modules. Bull. London Math. Soc., 4, 151–155. [Chapters 1, 6].
[Eck00] Eckmann, B. 2000. Introduction to L2-methods in Topology. Israel J. Math., 117, 183–219. [Chapter 4].
[EiGa57] Eilenberg, S. and Ganea, T. 1957. On the Lusternik-Schnirelmann category of abstract groups. Ann. of Math., 65, 517–518. [Chapter 1].
[Eps61] Epstein, D. B. A. 1961. Finite presentations of groups and 3- manifolds. Quart. J. Math. Oxford Series, (2), 12. [Chapters 6, 7].
[Euf92] Eufinger, M. 1992. Normalformen für Q-Transformationen bei Präsentationen freier Produkte. Diplomarbeit, Frankfurt/Main (unpublished). [Chapter 7].
[Fox52] Fox, R. H. 1952. On the Complementary Domains of a Certain Pair of Inequivalent Knots. Indag. Math, 14, 37–40. [Chapter 5].
[FrYe89] Freyd, Peter, and Yetter, David. 1989. Brided compact closed Categories with applications to Low dimensional Topology. Advances in Mathematics, 77, 156–182. [Chapter 3].
[Geo08] Geoghegan, R. 2008. Topological Methods in Group Theory. Graduate Texts in Math., vol. 243. Springer-Verlag. [Chapters 1, 6].
[Gil76] Gildenhuys, D. 1976. Classification of solvable groups of cohomological dimension 2. Math. Z., 166, 21–25. [Chapters 1, 6].
[GlHo05] Glock, J., and Hog-Angeloni, C. I. 2005. Embeddings of 2-complexes into 3-manifolds. Journal of Knot Theory and Its Ramifications, 14 (1), 9–20. [Chapter 5].
[Gol99] Goldstein, R. Z. 1999. The length and thickness of words in a free group. Proc. of the Am. Math. Soc., 127 (10), 2857–2863. [Chapter 5].
[Gru76] Gruenberg, K. W. 1976. Relation Modules of Finite Groups. CBMS Regional Conference Series in Mathematics No. 25, AMS. [Chapters 1, 6].
[Gru80] Gruenberg, K. W. 1980. The partial Euler characteristic of the direct powers of a finite group. Arch. Math., 35, 267–274. [Chapters 1, 6].
[GrLi08] Gruenberg†, K., and Linnell, P. 2008. Generation gaps and abelianized defects of free products. J. Group Theory, 11 (5), 587–608. [Chapters 1, 6, 7].
[Guo16] Guo, Guangyuan. 2016. Heegaard diagrams of S 3 and the Andrews- Curtis Conjecture. arXiv:1601.06871. [Chapter 2].
[Har93] Harlander, J. 1993. Solvable groups with cyclic relation module. J. Pure Appl. Algebra, 190, 189–198. [Chapter 1].
[Har96] Harlander, J. 1996. Closing the relation gap by direct product stabilization. J. Algebra, 182, 511–521. [Chapters 1, 6].
[Har97] Harlander, J. 1997. Embeddings into efficient groups. Proc. Edinburgh Math. Soc., 40, 314–324. [Chapters 1, 6].
[Har00] Harlander, J. 2000. Some aspects of efficiency. Pages 165–180 of: Baik, Johnson, and Kim (eds), Groups–Korea 1998, Proceedings of the 4th international conference, Pusan, Korea. Walter deGruyter. [Chapters 1, 6].
[HaHoMeRo00] Harlander, J., Hog-Angeloni, C., Metzler, W., and Rosebrock, S. 2000. Problems in Low-dimensional Topology. Encyclopedia of Mathematics Supplement II (ed. M. Hazewinkel). Kluwer Academic Publishers. [Chapter 1].
[HaJe06] Harlander, J., and Jensen, J. A. 2006. Exotic relation modules and homotopy types for certain 1-relator groups. Algebr. Geom. Topol., ü, 2163–2173. [Chapter 1].
[HaMi10] Harlander, J., and Misseldine, A. 2010. On the K-theory and homotopy theory of the Klein bottle group. Homology, Homotopy, and Applications, 12(2), 1–10. [Chapter 1].
[HaRo03] Harlander, J., and Rosebrock, S. 2003. Generalized knot complements and some aspherical ribbon disc complements. Knot theory and its Ramifications, 12 (7), 947–962. [Chapter 4].
[HaRo10] Harlander, J., and Rosebrock, S. 2010. On distinguishing virtual knot groups from knot groups. Journal of Knot Theory and its Ramifications, 19 (5), 695–704. [Chapter 4].
[HaRo12] Harlander, J., and Rosebrock, S. 2012. On Primeness of Labeled Oriented Trees. Knot theory and its Ramifications, 21 (8). [Chapter 4].
[HaRo15] Harlander, J., and Rosebrock, S. 2015. Aspherical Word Labeled Oriented Graphs and cyclically presented groups. Knot theory and its Ramifications, 24 (5). [Chapter 4].
[HaRo17] Harlander, J., and Rosebrock, S. 2017. Injective labeled oriented trees are aspherical. arXiv:1212.1943, to appear in: Mathematische Zeitschrift. [Chapter 4].
[Hig51] Higman, G. 1951. A finitely generated infinite simple group. J. London Math. Soc., 26, 61–64. [Chapter 1].
[Hil97] Hillman, J. A. 1997. L2-homology and asphericity. Israel J. Math., 99, 271–283. [Chapter 4].
[Han05] Hansel, J. 2005. Andrews-Curtis-Graphen endlicher Gruppen. Diplomarbeit, Frankfurt (unpublished). [Chapter 2].
[Ho-AnMa08] Hog-Angeloni, C., and Matveev, S. 2008. Roots in 3-manifold topology. Pages 295–319 of: The Zieschang Gedenkschrift, Geom. Topol. Monogr., vol. 14. Geometry and Topology Publications, Coventry. [Chapter 5].
[Ho-AnMe04] Hog-Angeloni, C., and Metzler, W. 2004. Ein Überblick über Resultate und Aktivitäten zum Andrews-Curtis-Problem. preprint, Frankfurt. [Chapter 2].
[Ho-AnMe06] Hog-Angeloni, C., and Metzler, W. 2006. Strategies towards a disproof of the general Andrews-Curtis Conjecture. Siberian Electronic Mathematical Reports, 3. [Chapter 2].
[How99] Howie, J. 1999. Bestvina-Brady Groups and the Plus Construction. Math. Proc. Cambridge Phil. Soc., 127, 487–493. [Chapters 1, 4, 6].
[Hu01] Hu, Sen. 2001. Lecture notes on Chern-Simons-Witten Theory. World Scientific (Wspc). [Chapter 3].
[HuRo95] Huck, G., and Rosebrock, S. 1995. Weight tests and hyperbolic groups. Pages 174–183 of: A., Duncan, N., Gilbert, J., Howie (ed), Combinatorial and Geometric Group Theory. London Math. Soc. Lecture Note Ser., vol. 204. London: Cambridge University Press. [Chapter 4].
[HuRo00] Huck, G., and Rosebrock, S. 2000. Cancellation Diagrams with nonpositive Curvature. Pages 128–149 of: et al., Michael, Atkinson (ed), Computational and Geometric Aspects of Modern Algebra. London Math. Soc. Lecture Note Ser., vol. 275. London: Cambridge University Press. [Chapter 4].
[HuRo01] Huck, G., and Rosebrock, S. 2001. Aspherical Labelled Oriented Trees and Knots. Proceedings of the Edinburgh Math. Soc. 44, 285– 294. [Chapter 4].
[HuRo07] Huck, G., and Rosebrock, S. 2007. Spherical Diagrams and Labelled Oriented Trees. Proceedings of the Edinburgh Math. Soc., 137A, 519–530. [Chapter 4].
[Joh97] Johnson, D.L. 1997. Presentations of Groups, 2nd edition. LMS Student Texts, vol. 15. Cambridge University Press. [Chapters 1, 6].
[Joh03] Johnson, F.E.A. 2003. Stable Modules and the D(2)-Problem. London Math. Soc. Lecture Note Ser., vol. 301. Cambridge University Press. [Chapter 1].
[Joh12] Johnson, F.E.A. 2012. Syzygies and Homotopy Theory. Algebra and Applications, vol. 17. London: Springer-Verlag. [Chapter 1].
[Kad10] Kaden, H. 2010. Considerations about the Andrews-Curtis invariants based on sliced 2-complexes. arXiv math. GT. [Chapter 3].
[Kad17] Kaden, H. 2017. Considerations for constructing Andrews-Curtis invariants of s-move 3-cells. arXiv math. GT. [Chapter 3].
[KaMaSo60] Karrass, A., Magnus, W., and Solitar, D. 1960. Elements of finite order in groups with a single defining relation. Comm. Pure Appl. Math., 13, 57–66. [Chapter 7].
[KaRo96] Kaselowsky, A., and Rosebrock, S. 1996. On the Impossibility of a Generalization of the HOMFLY – Polynomial to labelled Oriented Graphs. Annales de la Facult'e des Sciences de Toulouse V, 3, 407–419. [Chapter 4].
[Kau87] Kauffman, Louis H. 1987. On knots. Annals of Mathematics Studies, vol. 115. Princeton University Press, Princeton, NJ. [Chapter 3].
[Kau99] Kauffman, Louis H. 1999. Virtual knot theory. European Journal of Combinatorics, 20 (7), 663–690. [Chapters 4, 5].
[Kin07a] King, Simon A. 2007a. Ideal Turaev-Viro invariants. Topology Appl., 154(6), 1141–1156. [Chapter 3].
[Kin07b] King, Simon A. 2007b. Verschiedene Anwendungen kombinatorischer und algebraischer Strukturen in der Topologie. [Chapter 3].
[Kly93] Klyachko, A. 1993. A funny property of sphere and equations over groups. Communications in Algebra, 21 (7), 2555–2575. [Chapter 4].
[Kne29] Kneser, H. 1929. Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten. J. Dtsch. Math. Verein, 38, 248–260. [Chapter 5].
[KoMa11] Korablev, F. G., and Matveev, S. V. 2011. Reduction of knots in thickened surfaces and virtual knots. Dokl. Math., 83 (2), 262–264. [Chapter 5].
[KrRo00] Kreuzer, Martin, and Robbiano, Lorenzo. 2000. Computational commutative algebra. Springer-Verlag, Berlin. [Chapter 3].
[Kor15] Korner, J. 2015. Das Relatorenlückenproblem für freie Produkte. Masterarbeit, Frankfurt/Main, unpublished. [Chapter 7].
[Kuh00a] Kuhn, A. 2000a. extract from: Stabile Teilkomplexe und Andrews-Curtis-Operationen. Diplomarbeit, Frankfurt/Main. http://www.cambridge.org/9781316600900, [Chapter 2].
[Kuh00b] Kuhn, A. 2000b. Stabile Teilkomplexe und Andrews-Curtis- Operationen. Diplomarbeit, Frankfurt/Main (unpublished). [Chapter 2].
[Luc01] Luck, W. 2001. L2-invariants: Theory and Applications to Geometry and K-Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, Volume 44, Springer. [Chapter 4].
[Li00] Li, Zhongmou. 2000. Heegaard-Diagrams and Applications. PhDthesis, university of British Columbia. [Chapter 2].
[Lis17] Lishak, B. 2017. Balanced finite presentations of the trivial group. Journal of Topology and Analysis, 9 (2), 363–378. [Chapter 2].
[LiNa17] Lishak, B., and Nabutovsky, A. 2017. Balanced presentations of the trivial group and four-dimensional geometry. Journal of topology and analysis, 9 (1), 27–49. [Chapter 2].
[Lou15] Louder, L. 2015. Nielsen equivalence in closed surface groups. arXiv:1009.0454v2. [Chapter 1].
[Luf96] Luft, E. 1996. On 2-dimensional aspherical complexes and a problem of J. H. C. Whitehead. Math. Proc. Camb. Phil. Soc., 119, 493–495. [Chapter 4].
[Lus95] Lustig, M. 1995. Non-efficient torsion free groups exist. Comm. Algebra, 23, 215–218. [Chapters 1, 6].
[MaKaSo76] Magnus, W., Karras, A., and Solitar, D. 1976. Combinatorial Group Theory. Dover Publications. [Chapter 1].
[Man80] Mandelbaum, Richard. 1980. Four-dimensional topology: an introduction. bams. [Chapter 3].
[Man07a] Mannan, W. H. 2007a. The D(2) property for D8. Algebraic & Geometric Topology, 7, 517–528. [Chapter 1].
[Man07b] Mannan, W. H. 2007b. Homotopy types of truncated projective resolutions. Homology, Homotopy and Applications, 9(2), 445–449. [Chapter 1].
[Man09] Mannan, W. H. 2009. Realizing algebraic 2-complexes by cell complexes. Math. Proc. Cambridge Math. Soc., Issue 03, 146, Issue 03, 671–673. [Chapter 1].
[Man13] Mannan, W. H. 2013. A commutative version of the group ring. J. Algebra, 379, 113–143. [Chapter 1].
[MaO'S13] Mannan, W. H., and O'Shea, S. 2013. Minimal algebraic complexes over D4n. Algebraic & Geometric Topology, 13, 3287–3304. [Chapter 1].
[Man16] Mannan, Wajid H. 2016. Explicit generators of the relation module in the example of Gruenberg-Linell. Math. Proc. Cambridge Philos. Soc., 161 (2), 199–202. [Chapter 7].
[Mat03] Matveev, S. 2003. Algorithmic Topology and Classification of 3- Manifolds. Algorithms and Computations in Mathematics, vol. 9. Springer Verlag New York, Heidelberg, Berlin. [Chapters 2, 3].
[Mat12a] Matveev, S. 2012a. Prime decomposition of knots in T × I. Topology Appl., 159 (7), 1820–1824. [Chapter 5].
[Mat12b] Matveev, S. 2012b. Roots and decompositions of three-dimensional manifolds. Russiam Math. Surveis, 67 (3), 1459–507. [Chapter 5].
[MaTu11] Matveev, S., and Turaev, V. 2011. A semigroup of theta-curves in 3-manifolds. Mosc. Math. J., 11 (4), 805–814. [Chapter 5].
[Mat10] Matveev, S. V. 2010. On prime decompositions of knotted graphs and orbifolds. Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia, 57, 89–96. [Chapter 5].
[MaSo96] Matveev, Sergei V., and Sokolov, Maxim V. 1996. On a simple invariant of Turaev-Viro type. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 234 (Differ. Geom. Gruppy Li i Mekh. 15-1), 137–142, 263. [Chapter 3].
[Met00] Metzler, W. 2000. Verallgemeinerte Biasinvarianten und ihre Berechnung. Pages 192–207 of: Atkinson, M. et al. (ed), Computational and Geometric Aspects of Modern Algebra. London Math. Soc. Lecture Note Series, vol. 275. [Chapter 2].
[Mil62] Milnor, J. 1962. A unique factorisation theorem for 3-manifolds. Amer. J. Math., 84, 1–7. [Chapter 5].
[Mul00] Muller, Klaus. 2000. Probleme des Einfachen Homotopietyps in niederen Dimensionen und ihre Behandlung mit Hilfsmitteln der Topologischen Quantenfeldtheorie. Der Andere Verlag Dissertation Frankfurt/Main. [Chapter 3].
[Mut11] Muth, C. 2011. Relatorenlücke und vermutete Beispiele. Masterarbeit, Mainz unpublished. [Chapter 7].
[Nab12] Naber, Greg. 2012. Yang-Mills to Seiberg-Witten via TQFT The Witten Conjecture. preprint, Black Hills State University. [Chapter 3].
[New42] Newman, M. H. A. 1942. On theories with a combinatorial definition of ‘equivalence’. Ann. of Math., (2) 43:2, 223–243. [Chapter 5].
[O'S12] O'Shea, S. 2012. The D(2)-problem for dihedral groups of order 4n. Algebraic & Geometric Topology, 12, 2287–2297. [Chapter 1].
[Osi15] Osin, D. 2015. On acylindrical hyperbolicity of groups with positive first 2-Betti number. Bull. London Math. Soc. 47, 5, 725–730. [Chapter 4].
[OsTh13] Osin, D., and Thom, A. 2013. Normal generation and 2-betti numbers of groups. Math. Ann., 355 (4), 1331–1347. [Chapters I, IV].
[Per02] Perelman, G. 2002. The entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159. [Chapter 2].
[Per03a] Perelman, G. 2003a. Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. arXiv:math.DG/0307245. [Chapter 2].
[Per03b] Perelman, G. 2003b. Ricci flow with surgery on three-manifolds. arXiv:math.DG/0303109. [Chapter 2].
[Pet07] Petronio, C. 2007. Spherical splitting of 3-orbifolds. Math. Proc. Cambridge Philos. Soc., 142, 269–287. [Chapter 5].
[Poe13] Poelstra, Andrew. 2013. A brief Overview of Topological Quantum Field Theory. preprint. [Chapter 3].
[Qui76] Quillen, D. 1976. Projective modules over polynomial rings. Invent. Math., 36, 167–171. [Chapter 1].
[Qui92] Quinn, Frank. 1992. Lectures on Axiomatic Quantum Field Theory. preprint. [Chapter 3].
[Qui95] Quinn, Frank. 1995. Lectures on Axiomatic Quantum Field Theory. IAS/Park City Mathematical series, 1. [Chapter 3].
[Rep88] Repovs, D. 1988. Regular neighbourhoods of homotopically PL embedded compacta in 3-manifolds. Suppl. Rend. Circ. Mat. Palermo, 18, 213–243. [Chapter 5].
[Ros94] Rosebrock, S. 1994. On the Realization of Wirtinger Presentations as Knot Groups. Journal of Knot Theory and its Ramifications, 3 (2), 211 – 222. [Chapter 4].
[Ros00] Rosebrock, S. 2000. Some aspherical labeled oriented graphs. Pages 307–314 of: Matveev, S. (ed), Low-Dimensional Topology and Combinatorial Group Theory. Proceedings of the International Conference, Kiev. [Chapter 4].
[Ros07] Rosebrock, S. 2007. The Whitehead-Conjecture – an Overview. Siberian Electronic Mathematical Reports, 4, 440–449. [Chapter 4].
[Ros10] Rosebrock, S. 2010. On the Complexity of labeled oriented trees. Proc. of the Indian Acad. of Sci, 120 (1), 11–18. [Chapter 4].
[Ros02] Rosson, John. 2002. Multiplicative Invariants of Special 2- Complexes. Ph.D. thesis, Department of Mathematics, Portland State University, unpublished. [Chapter 3].
[Rot02] Rotman, J. J. 2002. Advanced Modern Algebra. Prentice Hall. [Chapters 1, 6].
[Sch49] Schubert, H. 1949. Die eindeutige Zerlegbarkeit eines Knotens in Primknoten. S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl., 3, 57– 104. [Chapter 5].
[Sta85] Stafford, J. T. 1985. Stably free, projective right ideals. Compositio Math., 54, 63–78. [Chapter 1].
[Sta99] Stallings, J. 1999. Whitehead Graphs on handlebodies. Geom. group theory down under (Canberra 1996) edn. de Gruyter, Berlin. [Chapter 5]. Pages 317–330.
[Sta68] Stallings, J. R. 1968. On torsion-free groups with infinitely many ends. Ann. of Math., 88, 312–334. [Chapter 1].
[Sta87] Stallings, John. 1987. A graph-theoretic lemma and groupembeddings. Pages 145–155 of: Gersten, S.M., and Stallings, J.R. (eds), Combinatorial group theory and topology. Annals of Mathematics Studies, vol. 111. [Chapter 4].
[Str74] Strebel, R. 1974. Homological methods applied to the derived series of groups. Comment. Math. Helv., 49, 63–78. [Chapter 1].
[Swa60] Swan, R. G. 1960. Periodic resolutions for finite groups. Ann. of Math. (2), 72, 267–291. [Chapter 1].
[Swa69] Swan, R. G. 1969. Groups of cohomological dimension one. J. Algebra, 12, 585–601. [Chapter 1].
[Swa83] Swan, R. G. 1983. Projective modules over binary polyhedral groups. J. Reine Angew. Math., 342, 66–172. [Chapter 1].
[Swa70] Swarup, G. A. 1970. Some properties of 3-manifolds with boundary. Quart. J. Math. Oxford Ser., (2) 21:1, 1–23. [Chapter 5].
[ThSe30] Threlfall, W., and Seifert, H. 1930. Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes I. Math. Ann., 104, 1–70. [Chapter 1].
[ThSe32] Threlfall, W., and Seifert, H. 1932. Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes II. Math. Ann., 107, 543–586. [Chapter 1].
[TuVi92] Turaev, V., and Viro, O. 1992. State Sum Invariants of 3-manifolds and Quantum 6j-symbols. Topology, 31 (4), 865–902. [Chapter 3].
[Tur94] Turaev, V. G. 1994. Quantum invariants of knots and 3-manifolds. de Gruyter Studies in Mathematics, vol. 18. Walter de Gruyter & Co., Berlin. [Chapter 3].
[Tut61] Tutte, W. 1961. A theory of 3-connected graphs. Ind. Math., 29, 441–455. [Chapter 5].
[Tut63] Tutte, W. 1963. How to draw a graph. Proc. London Math. Soc. (3), 13, 743–768. [Chapter 5].
[Vir10] Virelizier, Alexis. 2010. Quantum invariants of 3-manifolds, TQFTs, and Hopf monads. Habilitation a Diriger des recherches Universite Montpellier 2. [Chapter 3].
[Wald68] Waldhausen, F. 1968. Heegaard-Zerlegungen der 3-Sphäre. Topology, 7, 195–203. [Chapter 2].
[Wall66] Wall, C. T. C. 1966. Finiteness conditions for CW-complexes II. Proc. Roy. Soc. London Ser. A, 295, 129–139. [Chapter 1].
[Wam70] Wamsley, J. W. 1970. The multiplier of finite nilpotent groups. Bull. Austral. Math. Soc. 3, 1–8. [Chapters 1, 6].
[Whi36a] Whitehead, J. H. C. 1936a. On certain sets of elements in a free group. Proc. London Math. Soc., 41, 48–56. [Chapter 5].
[Whi36b] Whitehead, J. H. C. 1936b. On equivalent sets of elements in a free group. Annals of Math., 37, 782–800. [Chapter 5].
[Whi39] Whitehead, J. H. C. 1939. On the asphericity of regions in a 3-sphere. Fund. Math., 32, 149–166. [Chapter 4].
[Whi32a] Whitney, H. 1932a. Congruent graphs and the connectivity of graphs. Amer. J. Math., 54, 150–168. [Chapter 5].
[Whi32b] Whitney, H. 1932b. Non-separable and planar graphs. Trans. Amer. Math. Soc., 34, 339–362. [Chapter 5].
[Whi33a] Whitney, H. 1933a. 2-Isomorphic graphs. Amer. J. Math., 55, 245– 254. [Chapter 5].
[Whi33b] Whitney, H. 1933b. On the classification of graphs. Amer. J. Math., 55, 236–244. [Chapter 5].
[Whi33c] Whitney, H. 1933c. A set of topological invariants for graphs. Amer. J. Math., 55, 231–235. [Chapter 5].
[Zen05] Zentner, Stefanie. 2005. Wurzeln von Cobordismen und die Andrews- Curtis-Vermutung. Diplomarbeit Frankfurt/Main (unpublished). [Chapter 5].
[Zie70] Zieschang, H. 1970. Über die Nielsensche Kürzungsmethode in freien Produkten mit Amalgam. Invent. Math., 10, 4–37. [Chapter 7].

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