The Reidemeister number of any automorphism of a Gromov hyperbolic group is infinite.

DOI10.1023/B:JOTH.0000008749.42806.e3zbMath1070.20050arXivmath/0101010MaRDI QIDQ1781294

Alexander Fel'shtyn

Publication date: 23 June 2005

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0101010

zbMATH Keywords

automorphismstwisted conjugacy classesReidemeister numbersGromov hyperbolic groups

Mathematics Subject Classification ID

Automorphisms of infinite groups (20E36) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20) Fundamental group, presentations, free differential calculus (57M05) Hyperbolic groups and nonpositively curved groups (20F67) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (17)

The \(R_\infty\) and \(S_\infty\) properties for linear algebraic groups ⋮ Twisted conjugacy in classical Chevalley groups over certain domains of positive characteristic ⋮ Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups ⋮ On the automorphism group of generalized Baumslag-Solitar groups. ⋮ The \(R_\infty\)-property for right-angled Artin groups ⋮ The \(R_\infty\) property for pure Artin braid groups ⋮ The \(\mathrm{R}_\infty\)-property for nilpotent quotients of Baumslag-Solitar groups ⋮ Twisted conjugacy classes in nilpotent groups. ⋮ The \(R_\infty\)-property for Chevalley groups of types \(B_l\), \(C_l\), \(D_l\) over integral domains. ⋮ Twisted conjugacy in big mapping class groups ⋮ Automorphisms of the generalized Thompson's group Tn,r$T_{n,r}$ ⋮ Orbit decidability and the conjugacy problem for some extensions of groups ⋮ Twisted Burnside-Frobenius theory for virtually polycyclic groups. ⋮ New directions in Nielsen-Reidemeister theory ⋮ Twisted conjugacy and quasi-isometric rigidity of irreducible lattices in semisimple Lie groups ⋮ Reidemeister spectrum of special and general linear groups over some fields contains 1 ⋮ Twisted conjugacy in direct products of groups

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