The Reidemeister and Nielsen zeta functions
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 6, Tome 167 (1988), pp. 164-168
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In this paper we formulate a rationality theorem for the Reidemeister and Nielsen zeta-functions modulo a normal subgroup of the fundamental group. We give conditions under which these zeta-functions coincide. We formulate a conjecture aboutentropy for the Reidemeister numbers. We show that the radius of convergence of the Nielsen zeta-function for an orientation-preserving homeomorphism $f$ of a compact surface is an invariant of a three-dimensional manifold, the torus of the map $f$, and a special flow on it. In special cases we derive a functional equation for the Nielsen zeta-function. We give an example of a transcendental Nielsen zeta function.
@article{ZNSL_1988_167_a12,
author = {A. L. Fel'shtyn},
title = {The {Reidemeister} and {Nielsen} zeta functions},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {164--168},
publisher = {mathdoc},
volume = {167},
year = {1988},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_167_a12/}
}
A. L. Fel'shtyn. The Reidemeister and Nielsen zeta functions. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 6, Tome 167 (1988), pp. 164-168. http://geodesic.mathdoc.fr/item/ZNSL_1988_167_a12/