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Reidemeister torsion and dynamical zeta functions in Nielsen theory
by
Alexander Fel'shtyn
E.-M.-Arndt-Universität Greifswald, Germany
We give a survey of our results about dynamical zeta function in Nielsen theory and their
connections with the Reidemeister torsion.
We obtain an expression for the Reidemeister torsion
of the mapping torus of the dual map of a group
endomorphism, in terms of the Reidemeister zeta function of
the endomorphism.The result is obtained by expressing the Reidemeister zeta function in terms
of the Lefschetz zeta function of the dual map.
What this means is that the Reidemeister torsion counts the Nielsen fixed point classes
of all iterates of map i.e. periodic point classes of map.
Part of our results is joint work with Violetta Pilyugina and Richard Hill.
References: Fel'shtyn A.L.Pilyugina V.B., The Nielsen zeta function. Funct. Anal. Appl. v. 19, n.4, 1985, p. 61 -67. Fel'shtyn A.L. , Hill R.The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion. K-theory, v.8, n.4, 1994, p.367-393. Fel'shtyn A.L. , Hill R. Trace formulae, zeta functions, congruences and Reidemeister torsion in Nielsen theory. Forum Mathematicum, v.10, n.6, 1998, 641-663. Fel'shtyn A.L. Dynamical zeta functions, Nielsen theory and Reidemeister torsion. Habilitation, Greifswald, 1998.
Date received: April 26, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacy-02.