Automorphisms of surface braid groups

Elmas Irmak
Department of Mathematics
University of Michigan
Ann Arbor, MI 48109-1109

Nikolai V. Ivanov
Department of Mathematics
Michigan State University
E. Lansing, MI 48824-1027

John D. McCarthy
Department of Mathematics
Michigan State University
E. Lansing, MI 48824-1027

November 13, 2003

Let S be a closed, orientable,connected surface of genus g. Let n be a positive integer. Then-string surface braid group of S, denoted B_n(S),is the fundamental group of the space of unordered n-tuples of distinctpoints on S. Let {x₁,..., x_n} be the chosenbasepoint for B_n(S). We prove that every automorphism ofB_n(S) is induced by a self-homeomorphism of the pair (S,{x₁,..., x_n}) provided that g > 1 and n >2. This result establishes for the relevant surface braid groups what hasbeen previously established for surface mapping class groups and Torelli groups.