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

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.

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