Automorphisms of surface braid groups

Abstract

In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface of genus at least 2, and the number of strings is at least three. This result generalizes previous results for classical braid groups, mapping class groups, and Torelli groups.

21 pages, 0 figures

Cited by in corpus (9)

• Automorphisms of Torelli groups
• OE and W* superrigidity results for actions by surface braid groups
• Homomorphisms between braid groups
• Aspects of quantum gravity
• Injections of Artin groups
• Examples of centralizers in the Artin braid groups
• Braid groups are almost co-Hopfian
• Lower central series, surface braid groups, surjections and permutations
• Surjective homomorphisms between surface braid groups