Delta-structures on mapping class groups and braid groups

Abstract

We describe a Delta-group structure on the mapping class groups of surfaces, and show that it is compatible with the Delta-group structures of the braid groups of surfaces given by Berrick-Cohen-Wong-Wu. We then prove an isomorphism theorem relating these two Delta-groups. This is the first of a pair of papers on this topic. © 2013 American Mathematical Society Reverts to public domain 28 years from publication.