Twisted Burnside-Frobenius theory for discrete groups

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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.
17 pages, no figures, v2: some small improvements using referee's suggestions

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Group Theory, Number Theory, Operator Algebras, Representation Theory, 20Cxx; 20E45; 22D10; 22D25; 43A30; 46Lxx; 37C25; 54H25

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http://salesiana.dossiersoluciones.com/handle/123456789/102315

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606179
 http://arxiv.org/abs/math/0606179

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arXiv