The Reidemeister Number of Any Automorphism of a Gromov Hyperbolic Group is Infinite
By Alexander Fel'shtyn. 2001
83 citations recorded by the source corpus.
It is shown that the number of twisted conjugacy classes is infinite for any automorphism of a nonelementary, Gromov hyperbolic group. An analog of the Selberg theory for twisted conjugacy classes is suggested. Bibliography: 15 titles.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d21d0da01bfacceead2aceddaf783ffb8bb94d3e
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Twisted conjugacy classes in nilpotent groups (2007, background): “Lustig [24] showed implicitly that if p is finitely generated non-elementary Gromov hyperbolic then every automorphism j A AutðpÞ must have RðjÞ 1⁄4 y (see also [6]).”
- Twisted Conjugacy Classes in Exponential Growth Groups (2003, background): “In contrast to Fel’shtyn’s result [1], or to that of Levitt and Lustig [8], our counterexamples show that the growth rate does not determine the finiteness of R(φ).”
- Orbit decidability and the conjugacy problem for some extensions of groups (2007, background): “A couple of interesting results in this direction are that the number of ϕ -twisted conjugacy classes in a nonelementary word-hyperbolic group is always infinite (see [28] and [20]), and that there is an algorithm for recognizing ϕ -twisted conjugacy classes in free groups (see [7]).”