Twisted conjugacy classes in residually finite groups

Details Twisted conjugacy classes in residually finite groups Twisted conjugacy classes in residually finite groups

2012-04-14

arxiv.org/abs/1204.3175v1

Mathematics

Group Theory

20 pages, no figures

Scientific paper

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.

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