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Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

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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 S 2. This means that for any automorphism \({\phi}\) of G, where G is one of the above groups, the number of twisted \({\phi}\)-conjugacy classes is infinite.

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Authors and Affiliations

  1. Instytut Matematyki, Uniwersytet Szczecinski, ul.Wielkopolska 15, 70-451, Szczecin, Poland

    Alexander Fel’shtyn

  2. Boise State University, 1910 University Drive, Boise, ID, 83725-155, USA

    Alexander Fel’shtyn

  3. Department de Matemática, IME, USP, Caixa Postal 66.281, São Paulo, SP, CEP 05311-970, Brazil

    Daciberg L. Gonçalves

Authors
  1. Alexander Fel’shtyn
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  2. Daciberg L. Gonçalves
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Correspondence to Alexander Fel’shtyn.

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Fel’shtyn, A., Gonçalves, D.L. Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani). Geom Dedicata 146, 211–223 (2010). https://doi.org/10.1007/s10711-009-9434-6

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