Twisted conjugacy classes in residually finite groups
Group Theory
2012-05-01 v2 Dynamical Systems
Operator Algebras
Abstract
We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional irreducible unitary representations being invariant for the dual of this automorphism. Also, we prove that any finitely generated residually finite non-amenable group has the R-infinity property (any automorphism has infinitely many twisted conjugacy classes). This gives a lot of new examples and covers many known classes of such groups.
Cite
@article{arxiv.1204.3175,
title = {Twisted conjugacy classes in residually finite groups},
author = {Alexander Fel'shtyn and Evgenij Troitsky},
journal= {arXiv preprint arXiv:1204.3175},
year = {2012}
}
Comments
20 pages, no figures, v2: typos corrected, references added