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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk


IMPACT FACTOR increased in 2015: 1.616
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Rank 18 out of 312 in category Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

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1435-5345
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Twisted Burnside-Frobenius theory for discrete groups

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2007, Issue 613, Pages 193–210, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2007.097, February 2008

Publication History

Received:
2006-06-05
Revised:
2006-12-14
Published Online:
2008-02-05

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.

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[1]
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[2]
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