Automorphisms of braid groups on closed surfaces which are not S-2, T-2, P-2 or the Klein bottle

Zhang, Ping2016-04-052016-04-052006Zhang, 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/S0218216506005044Consider 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 S-2, T-2, P-2 or the Klein bottleAutomorphisms of Braid Groups on Closed Surfaces Which Are Not S2, T2, P2 or the Klein BottleArticle1591231124410.1142/S02182165060050442-s2.0-33845698291WOS:000243698800011Q4Q3