Geometry & Topology

The mapping class group of a manifold naturally acts on the homology of the manifold, though this action is often not faithful. However, its action on the homology of the configuration space “sees” more, in the sense that it has a smaller kernel. In this talk, I will discuss recent results on these actions and their kernels, both for general manifolds and in the specific case of surfaces. This is partially joint work with Bianchi and Looijenga.