Reidemeister numbers

Abstract

In [A. L. Fel’shtyn and R. Hill, < i> The Reidemeister zeta function with applications to Nielsen theory and connection with Reidemeister torsion< /i> , K-Theory < b> 8< /b> (1994), 367–393] we have conjectured that the Reidemeister number is infinite as long as an endomorphism of a discrete group is injective and the group has exponential growth. In the paper we prove this conjecture for any automorphism of a non-elementary, Gromov hyperbolic group. We also prove some generalisations of this result. The main results of the paper have topological counterparts.