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Topological and dynamical obstructions to extending group actions.

Presented by: 
Sam Nariman Northwestern University
Date: 
Friday 7th December 2018 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
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.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons