Geometry and Topology Seminar
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. If time permits, we also discuss cohomological obstruction to extending $SO(3)$ action on $S^2$ to certain $3$-manifolds that bound $S^2$. This is joint work with Kathryn Mann.