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Twisted Burnside-Frobenius theory for discrete groups

Alexander Fel'shtyn·Evgenij Troitsky
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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 f is equal to the number of finite-dimensional fixed points of the induced map f^ 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.

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BibTeXRIS

Alexander Fel'shtyn, Evgenij Troitsky. 2006-12-13. Twisted Burnside-Frobenius theory for discrete groups. https://arxiv.org/abs/math/0606179

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