Reidemeister numbers

Alexander Fel'shtyn

DOI: http://dx.doi.org/10.12775/TMNA.2003.009

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.

Keywords


Reidemeister number; twisted conjugacy classes; Gromov hyperbolic group; fundamental group

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