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Licensed Unlicensed Requires Authentication Published by De Gruyter February 5, 2008

Twisted Burnside-Frobenius theory for discrete groups

Alexander Fel'shtyn and Evgenij Troitsky
From the journal

Abstract

For a wide class of groups including polycyclic and finitely generated polynomial growth groups it is proved that the Reidemeister number of an automorphism is equal to the number of finite-dimensional fixed points of the induced map on the unitary dual, if one of these numbers is finite. This theorem is a natural generalization of the classical Burnside-Frobenius theorem to infinite groups. This theorem also has important consequences in topological dynamics and in some sense is a reply to a remark of J.-P. Serre. The main technical results proved in the paper yield a tool for a further progress.

Received: 2006-06-05
Revised: 2006-12-14
Published Online: 2008-02-05
Published in Print: 2007-12-19

© Walter de Gruyter