Twisted Conjugacy Classes in Symplectic Groups, Mapping Class Groups and Braid Groups (with an Appendix Written Jointly with Francois Dahmani)

Authors

Alexander Fel'shtyn, Boise State University
Daciberg L. Gonçalves, Department de Matemática, IME, USP

Document Type

Article

Publication Date

6-1-2010

Abstract

We prove that the symplectic group Sp(2n, ℤ) and the mapping class group Mod_S 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.

Publication Information

Fel'shtyn, Alexander and Gonçalves, Daciberg L.. (2010). "Twisted Conjugacy Classes in Symplectic Groups, Mapping Class Groups and Braid Groups (with an Appendix Written Jointly with Francois Dahmani)". Geometriae Dedicata, 146(1), 211-223. https://doi.org/10.1007/s10711-009-9434-6