Volume 17, issue 1 (2017)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
New topological methods to solve equations over groups

Anton Klyachko and Andreas Thom

Algebraic & Geometric Topology 17 (2017) 331–353
Abstract

We show that the equation associated with a group word w G F2 can be solved over a hyperlinear group G if its content — that is, its augmentation in F2 — does not lie in the second term of the lower central series of F2. Moreover, if G is finite, then a solution can be found in a finite extension of G. The method of proof extends techniques developed by Gerstenhaber and Rothaus, and uses computations in p–local homotopy theory and cohomology of compact Lie groups.

Keywords
equations over groups, cohomology of Lie groups
Mathematical Subject Classification 2010
Primary: 22C05, 20F70
References
Publication
Received: 8 December 2015
Revised: 23 March 2016
Accepted: 27 May 2016
Published: 26 January 2017
Authors
Anton Klyachko
Faculty of Mechanics and Mathematics
Moscow State University
Leninskie Gorki
Moscow
119991
Russia
Andreas Thom
Institut für Geometrie
TU Dresden
D-01062 Dresden
Germany