Volume 17, issue 1 (2017)

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New topological methods to solve equations over groups

Anton Klyachko and Andreas Thom

Algebraic & Geometric Topology 17 (2017) 331–353
Bibliography
1 D V Baranov, A A Klyachko, Economical adjunction of square roots to groups, Sibirsk. Mat. Zh. 53 (2012) 250 MR2975932
2 P F Baum, W Browder, The cohomology of quotients of classical groups, Topology 3 (1965) 305 MR0189063
3 A Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. 57 (1953) 115 MR0051508
4 A Borel, Sur l’homologie et la cohomologie des groupes de Lie compacts connexes, Amer. J. Math. 76 (1954) 273 MR0064056
5 R Bott, The space of loops on a Lie group, Michigan Math. J. 5 (1958) 35 MR0102803
6 R Bott, A note on the Samelson product in the classical groups, Comment. Math. Helv. 34 (1960) 249 MR0123330
7 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
8 M Edjvet, J Howie, The solution of length four equations over groups, Trans. Amer. Math. Soc. 326 (1991) 345 MR1002920
9 M Edjvet, A Juhász, Nonsingular equations over groups, II, Comm. Algebra 38 (2010) 1640 MR2642015
10 M Edjvet, A Juhász, Non-singular equations over groups, I, Algebra Colloq. 18 (2011) 221 MR2785779
11 A Elkasapy, A Thom, About Gotô’s method showing surjectivity of word maps, Indiana Univ. Math. J. 63 (2014) 1553 MR3283561
12 A Evangelidou, The solution of length five equations over groups, Comm. Algebra 35 (2007) 1914 MR2324624
13 S M Gersten, Reducible diagrams and equations over groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 15 MR919828
14 M Gerstenhaber, O S Rothaus, The solution of sets of equations in groups, Proc. Nat. Acad. Sci. USA 48 (1962) 1531 MR0166296
15 M Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. 1 (1999) 109 MR1694588
16 H Hamanaka, D Kishimoto, A Kono, Self homotopy groups with large nilpotency classes, Topology Appl. 153 (2006) 2425 MR2243721
17 A Hatcher, Algebraic topology, Cambridge University Press (2002) MR1867354
18 G Higman, A finitely generated infinite simple group, J. London Math. Soc. 26 (1951) 61 MR0038348
19 H Hopf, Über den Rang geschlossener Liescher Gruppen, Comment. Math. Helv. 13 (1940) 119 MR0004631
20 J Howie, On pairs of 2–complexes and systems of equations over groups, J. Reine Angew. Math. 324 (1981) 165 MR614523
21 J Howie, The solution of length three equations over groups, Proc. Edinburgh Math. Soc. 26 (1983) 89 MR695646
22 S V Ivanov, A A Klyachko, Solving equations of length at most six over torsion-free groups, J. Group Theory 3 (2000) 329 MR1772011
23 I James, E Thomas, Which Lie groups are homotopy-abelian ?, Proc. Nat. Acad. Sci. USA 45 (1959) 737 MR0106465
24 A Juhász, On the solvability of equations over groups, Comm. Algebra 32 (2004) 1487 MR2100369
25 D Kishimoto, A Kono, On a conjecture of Ōshima, Topology Appl. 156 (2009) 2189 MR2544124
26 A A Klyachko, A funny property of sphere and equations over groups, Comm. Algebra 21 (1993) 2555 MR1218513
27 A A Klyachko, Equations over groups, quasivarieties, and a residual property of a free group, J. Group Theory 2 (1999) 319 MR1696317
28 A A Klyachko, How to generalize known results on equations over groups, Mat. Zametki 79 (2006) 409 MR2251364
29 A A Klyachko, A V Trofimov, The number of non-solutions of an equation in a group, J. Group Theory 8 (2005) 747 MR2179667
30 F Levin, Solutions of equations over groups, Bull. Amer. Math. Soc. 68 (1962) 603 MR0142643
31 A Malcev, On isomorphic matrix representations of infinite groups, Mat. Sbornik N.S. 8 (50) (1940) 405 MR0003420
32 J P May, K Ponto, More concise algebraic topology: localization, completion, and model categories, University of Chicago Press (2012) MR2884233
33 M Mimura, G Nishida, H Toda, Localization of CW–complexes and its applications, J. Math. Soc. Japan 23 (1971) 593 MR0295347
34 B H Neumann, Adjunction of elements to groups, J. London Math. Soc. 18 (1943) 4 MR0008808
35 N Nikolov, D Segal, Generators and commutators in finite groups; abstract quotients of compact groups, Invent. Math. 190 (2012) 513 MR2995181
36 V G Pestov, Hyperlinear and sofic groups: a brief guide, Bull. Symbolic Logic 14 (2008) 449 MR2460675
37 G J Porter, Homotopical nilpotence of S3, Proc. Amer. Math. Soc. 15 (1964) 681 MR0169244
38 V K Rao, Spin(n) is not homotopy nilpotent for n 7, Topology 32 (1993) 239 MR1217066
39 V Roman’kov, Equations over groups, Groups Complex. Cryptol. 4 (2012) 191 MR3043434
40 O S Rothaus, On the non-triviality of some group extensions given by generators and relations, Ann. of Math. 106 (1977) 599 MR0467760
41 H Samelson, Groups and spaces of loops, Comment. Math. Helv. 28 (1954) 278 MR0065157
42 J P Serre, Groupes d’homotopie et classes de groupes abéliens, Ann. of Math. 58 (1953) 258 MR0059548
43 J P Serre, Trees, Springer (2003) MR1954121
44 A Stolz, A Thom, On the lattice of normal subgroups in ultraproducts of compact simple groups, Proc. Lond. Math. Soc. 108 (2014) 73 MR3162821
45 S Stolz, P Teichner, What is an elliptic object?, from: "Topology, geometry and quantum field theory" (editor U Tillmann), London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 247 MR2079378
46 A Thom, Convergent sequences in discrete groups, Canad. Math. Bull. 56 (2013) 424 MR3043070
47 B Weiss, Sofic groups and dynamical systems, Sankhyā Ser. A 62 (2000) 350 MR1803462
48 G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508
49 N Yagita, Homotopy nilpotency for simply connected Lie groups, Bull. London Math. Soc. 25 (1993) 481 MR1233412