Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 17, Number 1 (2017), 331-353.
New topological methods to solve equations over groups
We show that the equation associated with a group word can be solved over a hyperlinear group if its content — that is, its augmentation in — does not lie in the second term of the lower central series of . Moreover, if is finite, then a solution can be found in a finite extension of . The method of proof extends techniques developed by Gerstenhaber and Rothaus, and uses computations in –local homotopy theory and cohomology of compact Lie groups.
Algebr. Geom. Topol., Volume 17, Number 1 (2017), 331-353.
Received: 8 December 2015
Revised: 23 March 2016
Accepted: 27 May 2016
First available in Project Euclid: 16 November 2017
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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