Brunnian subgroups of mapping class groups and braid groups (Q2856119)

The authors continue their work exploring the relationship between Brunnian subgroups of mapping class groups and higher homotopy groups of spheres. They use previous work on a \(\Delta\)--structure on braid groups to obtain an explicit isomorphism between the higher homotopy groups of \(\Delta\)--groups of braid groups and the higher homotopy groups of the \(2\)--sphere. Furthermore, they obtain a short exact sequence relating the Brunnian subgroups of Riemann surfaces other than the sphere and \(\mathbb{RP}^2\) as the number of strands varies.