Twisted conjugacy classes in symplectic groups,mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani) |
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Authors: | Alexander Fel’shtyn Daciberg L Gonçalves |
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Institution: | (1) Department of Mathematics, University of the Aegean, Karlovassi, 832 00 Samos, Greece;(2) M. Sykiotis, Amalthias 18, 412 22 Larissa, Greece;(3) Present address: Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus |
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Abstract: | We prove that the symplectic group
Sp(2n,\mathbbZ){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 f{\phi} of G, where G is one of the above groups, the number of twisted f{\phi}-conjugacy classes is infinite. |
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Keywords: | |
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