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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
5-year IMPACT FACTOR: 1.690
Rank 18 out of 312 in category Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 3.614
Source Normalized Impact per Paper (SNIP) 2015: 1.901
Impact per Publication (IPP) 2015: 1.302

Mathematical Citation Quotient (MCQ) 2015: 1.53

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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

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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 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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