Automorphisms of braid groups on S2, T2, P2 and the Klein bottle K

Abstract

It is shown that for the braid group B-n(M) on a closed surface M of nonnegative Euler characteristic, Out(B-n(M)) is isomorphic to a group extension of the group of central automorphisms of B-n(M) by the extended mapping class group of M, with an explicit and complete description of Aut(B-n(S-2)), Aut(B-n(P-2)), Out(B-n(S-2)) and Out(B-n(P-2)).