Twisted Burnside-Frobenius theorem for discrete groups
by
Alexander Fel'shtyn
Boise State University
Coauthors: Evgenij Troitsky

It is proved for a wide class of groups including polycyclic and finitely generated polynomial growth groups that the Reidemeister number of an automorphism is equal to the number of finite-dimensional fixed points of induced map on the unitary dual space, if one of these numbers is finite. This theorem is a natural generalisation to infinite discrete groups of the classical Burnside-Frobenius theorem. On other hand it has important consequences in dynamics and topology. We also present some counterexamples to this statement for infinite discrete groups with extreme properties (HNN-group, Osin group, Ivanov group).

Paper reference: Preprint 46, Max-Planck-Institut fur Mathematik, 2005.

Date received: February 24, 2006