Twisted conjugacy classes in Symplectic groups, Mapping class groups and Braid groups(including an Appendix written with Francois Dahmani)

2007/08/20 by Alexander Fel’shtyn, Fel'shtyn, Alexander, Daciberg Lima Gonçalves +1
Mathematics · #20E45 #37C25 #55M20 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0708.2628

openalex publication_date 2007/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the symplectic group Sp(2n,\mathbb Z) and the mapping class group Mod_S of a compact surface S satisfy the R_∞ property. We also show that B_n(S), the full braid group on n-strings of a surface S, satisfies the R_∞ property in the cases where S is either the compact disk D, or the sphere S². This means that for any automorphism ϕ of G, where G is one of the above groups, the number of twisted ϕ-conjugacy classes is infinite.

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