Automorphisms of Braid Groups on Closed Surfaces Which Are Not S2, T2, P2 or the Klein Bottle

Zhang, Ping02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2016-04-052025-09-182016-04-052025-09-182006Zhang, P. (2006). Automorphisms of braid groups on closed surfaces which are not S-2, T-2, P-2 or the Klein bottle. Journal of Knot Theoryand Its Ramifications, 15(9), 1231-1244. http://dx.doi.org/10.1142/S02182165060050440218-2165https://doi.org/10.1142/S0218216506005044https://hdl.handle.net/20.500.12416/14373Consider a surface braid group of n strings as a subgroup of the isotopy group of homeomorphisms of the surface permuting n fixed distinguished points. Each automorphism of the surface braid group (respectively, of the special surface braid group) is shown to be a conjugate action on the braid group (respectively, on the special braid group) induced by a homeomorphism of the underlying surface if the closed surface, either orientable or non-orientable, is of negative Euler characteristic. In other words, the group of automorphisms of such a surface braid group is isomorphic to the extended mapping class group of the surface with n punctures, while the outer automorphism group of the surface braid group is isomorphic to the extended mapping class group of the closed surface itself.eninfo:eu-repo/semantics/closedAccessSurface BraidsAutomorphism Group Of A GroupSurface Of Negative Euler CharacteristicsMapping Class GroupAutomorphisms of Braid Groups on Closed Surfaces Which Are Not S2, T2, P2 or the Klein BottleAutomorphisms of braid groups on closed surfaces which are not S-2, T-2, P-2 or the Klein bottleArticle10.1142/S02182165060050442-s2.0-33845698291