Year: 2012
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Fel'shtyn, Alexander, Troitsky, Evgenij
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1789998202