The geometry of twisted conjugacy classes in wreath products

Abstract

We give a geometric proof based on recent work of Eskin, Fisher and Whyte that the lamplighter group $L_n$ has infinitely many twisted conjugacy classes for any automorphism $\vp$ only when $n$ is divisible by 2 or 3, originally proved by Gonçalves and Wong. We determine when the wreath product $G\wr \mathbb{Z}$ has this same property for several classes of finite groups $G$, including symmetric groups and some nilpotent groups.

19 pages, 4 figures

References in corpus (2)

• A note on twisted conjugacy and generalized Baumslag-Solitar groups
• Twisted conjugacy classes in Symplectic groups, Mapping class groups and Braid groups(including an Appendix written with Francois Dahmani)

Cited by in corpus (4)

• On the Reidemeister spectrum and the $R_{\infty }$ property for some free nilpotent groups
• On the $\Sigma$-invariants of wreath products
• Twisted conjugacy classes in nilpotent groups
• Property $R_{\infty }$ for some spherical and affine Artin-Tits groups