## Algebraic & Geometric Topology

### New topological methods to solve equations over groups

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 17, Number 1 (2017), 331-353.

Dates
Revised: 23 March 2016
Accepted: 27 May 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841315

Digital Object Identifier
doi:10.2140/agt.2017.17.331

Mathematical Reviews number (MathSciNet)
MR3604379

Zentralblatt MATH identifier
06680250

#### Citation

Klyachko, Anton; Thom, Andreas. New topological methods to solve equations over groups. Algebr. Geom. Topol. 17 (2017), no. 1, 331--353. doi:10.2140/agt.2017.17.331. https://projecteuclid.org/euclid.agt/1510841315

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