Topological and dynamical obstructions to extending group actions. – Sam Nariman (Northwestern University)

December 7, 2018 @ 11:30 am – 12:30 pm
Seminar Room 1
Newton Institute

For any 3-manifold $M$ with torus boundary, we find finitely generated subgroups of $Diff_0(partial M)$ whose actions do not extend to actions on $M$; in many cases, there is even no action by homeomorphisms. The obstructions are both dynamical and cohomological in nature. We also show that, if $partial M = S^2$, there is no section of the map $Diff_0(M) to Diff_0(partial M)$. This answers a question of Ghys for particular manifolds and gives tools for progress on the general program of bordism of group actions. This is a joint work with Kathryn Mann.