Trace formulae, Zeta functions, congruences and Reidemeister torsion in Nielsen theory
-
Alexander Fel'shtyn
and
Richard Hill
Abstract
In this paper we prove trace formulae for the Reidemeister number of a group endomorphism. This result implies the rationality of the Reidemeister zeta function in the following cases: the group is a direct product of a finite group and a finitely generated Abelian group; the group is finitely generated, nilpotent and torsion free. We connect the Reidemeister zeta function of an endomorphism of a direct product of a finite group and a finitely generated free Abelian group with the Lefschetz zeta function of the induced map on the unitary dual of the group. As a consequence we obtain a relation between a special value of the Reidemeister zeta function and a certain Reidemeister torsion. We also prove congruences for Reidemeister numbers of iterates of an endomorphism of a direct product of a finite group and a finitely generated free Abelian group which are the same as those found by Dold for Lefschetz numbers.
© Walter de Gruyter
Articles in the same Issue
- Trace formulae, Zeta functions, congruences and Reidemeister torsion in Nielsen theory
- Asymptotic estimates for best and stepwise approximation of convex bodies IV
- Partly divisible probability distributions
- Generalized curvature measures and singularities of sets with positive reach
- Representation type of finite rank almost completely decomposable groups
- Collineations of smooth stable planes
Articles in the same Issue
- Trace formulae, Zeta functions, congruences and Reidemeister torsion in Nielsen theory
- Asymptotic estimates for best and stepwise approximation of convex bodies IV
- Partly divisible probability distributions
- Generalized curvature measures and singularities of sets with positive reach
- Representation type of finite rank almost completely decomposable groups
- Collineations of smooth stable planes
