Algebra/Topology seminar

Speaker: Erik Lindell

Tilte: Stable cohomology of Torelli groups

Abstract: The Torelli group of a compact, orientable surface is the subgroup of its mapping class group that acts trivially on the homology of the surface. The cohomology of this group is quite poorly understood, even stably, i.e. when the genus of the surface is large compared to the cohomological degree. The first stable cohomology group was computed by Johnson in the early 80's, but since then little progress has been made until quite recently. In this talk, I will review some of these more recent developments, as well as similar results of my own and other authors for IA-automorphism groups, which are the analogously defined subgroups of automorphism groups of finitely generated free groups. If time permits, I will also discuss some work in progress aimed at producing similar results for Torelli groups of handlebodies.