Brunnian subgroups of mapping class groups and braid groups

Abstract

This is the second of a pair of papers on the Delta-group structure on the braid and mapping class groups of a surface. We obtain a description of the homotopy groups of these Delta-groups and generalize to an arbitrary surface the Berrick-Cohen-Wong-Wu exact sequence relating the Brunnian braid groups of the 2-sphere to its homotopy groups. We prove a similar result for Brunnian mapping class groups. © 2013 London Mathematical Society.