Topology Seminar: Ulrike Tillmann

Homology stability for families of discrete groups such as the symmetric groups, linear groups, braid groups and mapping class groups are well-known. Extensions to diffeomorphism groups of manifolds more generally have only been proved recently in a few special cases. We will revisit some classical results on configuration spaces, extend them to the equivariant setting, and prove homology stability for so-called symmetric diffeomorphism groups for arbitrary manifolds.