Twisted conjugacy classes of automorphisms of Baumslag-Solitar groups

dc.creatorFel'shtyn, Alexander
dc.creatorGoncalves, Daciberg L.
dc.date2004-05-31
dc.date2007-07-10
dc.date.accessioned2026-07-07T08:14:44Z
dc.date.available2026-07-07T08:14:44Z
dc.descriptionLet $ϕ:G \to G$ be a group endomorphism where $G$ is a finitely generated group of exponential growth, and denote by $R(ϕ)$ the number of twisted $ϕ$-conjugacy classes. Fel'shtyn and Hill \cite{fel-hill} conjectured that if $ϕ$ is injective, then $R(ϕ)$ is infinite. This conjecture is true for automorphisms of non-elementary Gromov hyperbolic groups, see \cite{ll} and \cite {fel:1}. It was showed in \cite {gw:2} that the conjecture does not hold in general. Nevertheless in this paper, we show that the conjecture holds for the Baumslag-Solitar groups $B(m,n)$, where either $|m|$ or $|n|$ is greater than 1 and $|m|\ne |n|$. We also show that in the cases where $|m|=|n|>1$ or $mn=-1$ the conjecture is true for automorphisms. In addition, we derive few results about the coincidence Reidemeister number.
dc.description20 pages, new sections 6 and 7 are added
dc.identifierhttps://arxiv.org/abs/math/0405590
dc.identifierhttp://arxiv.org/abs/math/0405590
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133234
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20E45; 37C25; 55M20
dc.titleTwisted conjugacy classes of automorphisms of Baumslag-Solitar groups
dc.typetext

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