Geometriae Dedicata

, Volume 146, Issue 1, pp 211–223 | Cite as

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

  • Alexander Fel’shtynEmail author
  • Daciberg L. Gonçalves
Original Paper


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.


Reidemeister number Twisted conjugacy classes Braids group Mapping class group Symplectic group 

Mathematics Subject Classification (2000)

20E45 37C25 55M20 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Alexander Fel’shtyn
    • 1
    • 2
    Email author
  • Daciberg L. Gonçalves
    • 3
  1. 1.Instytut MatematykiUniwersytet SzczecinskiSzczecinPoland
  2. 2.Boise State UniversityBoiseUSA
  3. 3.Department de MatemáticaIME, USPSão PauloBrazil

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