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

الأصل · EN

We prove that the symplectic group Sp(2n,Z) and the mapping class group Modₛ of a compact surface S satisfy the R∞ property. We also show that Bₙ(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.