Conjugacy classes of solutions to equations and inequations over hyperbolic groups

Details Conjugacy classes of solutions to equations and inequations over hyperbolic groups Conjugacy classes of solutions to equations and inequations over hyperbolic groups

2007-10-09

arxiv.org/abs/0710.1892v2

Mathematics

Group Theory

28 pages; referee's comments incorporated; to appear in the Journal of Topology

Scientific paper

We study conjugacy classes of solutions to systems of equations and inequations over torsion-free hyperbolic groups, and describe an algorithm to recognize whether or not there are finitely many conjugacy classes of solutions to such a system. The class of immutable subgroups of hyperbolic groups is introduced, which is fundamental to the study of equations in this context. We apply our results to enumerate the immutable subgroups of a torsion-free hyperbolic group.

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