Twisted Burnside-Frobenius theory for discrete groups

By Alexander Fel'shtyn, E. Troitsky. 2006

63 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/65708d00ae8a03561dc550735dcdc2f12d5aa3df

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In Geometry and Topology

1. Daciberg Lima Gonçalves
2. Peter Wong

In Mathematical Physics

1. Peter Wong
2. Daciberg Lima Gonçalves

Citations in the corpus

• Twisted conjugacy classes in nilpotent groups (2007, background): “[ 12 ].) In particular, groups that are quasi-isometric to”