Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion

• Autorzy: Alexander Fel'shtyn , Richard Hill
• 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1999
• Tom: 49
• Numer: 1
• Strony: 77-116

Daty

wydano

1999

Twórcy

autor

Alexander Fel'shtyn

• Fachbereich Mathematik, Universität Greifswald, Jahnstraße 15a, D-17487 Greifswald, Germany

autor

Richard Hill

• Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, D-5300 Bonn 3, Germany

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