Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2001; 38(6): 1107-1116

Printed November 1, 2001

Copyright © The Korean Mathematical Society.

Reidemeister zeta function for group extensions

Peter Wong

Bates College

Abstract

In this paper, we study the rationality of the Reidemeister zeta function of an endomorphism of a group extension. As an application, we give sufficient conditions for the rationality of the Reidemeister and the Nielsen zeta functions of selfmaps on an exponential solvmanifold or an infra-nilmanifold or the coset space of a compact connected Lie group by a finite subgroup.

Keywords: dynamical zeta function, Nielsen fixed point theory, homogeneous spaces, solvmanifolds, infra-nilmanifolds

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