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1999 | 49 | 1 | 77-116
Tytuł artykułu

Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we prove trace formulas for the Reidemeister numbers of group endomorphisms and the rationality of the Reidemeister zeta function in the following cases: the group is finitely generated and the endomorphism is eventually commutative; the group is finite; the group is a direct sum of a finite group and a finitely generated free Abelian group; the group is finitely generated, nilpotent and torsion free. We connect the Reidemeister zeta function of an endomorphism of a direct sum of a finite group and a finitely generated free Abelian group with the Lefschetz zeta function of the unitary dual map, and as a consequence obtain a connection of the Reidemeister zeta function with Reidemeister torsion. We also prove congruences for Reidemeister numbers which are the same as those found by Dold for Lefschetz numbers.
Słowa kluczowe
Rocznik
Tom
49
Numer
1
Strony
77-116
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Fachbereich Mathematik, Universität Greifswald, Jahnstraße 15a, D-17487 Greifswald, Germany
autor
  • Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, D-5300 Bonn 3, Germany
Bibliografia
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Typ dokumentu
Bibliografia
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