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New topological methods
to solve equations over groups
Anton Klyachko and Andreas Thom |
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Algebraic & Geometric Topology 17 (2017) 331–353
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Abstract |
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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. |
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Keywords
equations over groups, cohomology of Lie groups
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Mathematical Subject Classification 2010
Primary: 22C05, 20F70
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References |
Publication
Received: 8 December 2015
Revised: 23 March 2016
Accepted: 27 May 2016
Published: 26 January 2017
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Authors |
| Anton Klyachko | |
| Faculty of Mechanics and
Mathematics Moscow State University Leninskie Gory Moscow 119991 Russia |
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| Andreas Thom | |
| Institut für Geometrie TU Dresden D-01062 Dresden Germany |
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