Volume 17, issue 1 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 7, 2925–3415
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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