Frontiers in Mathematical Sciences
7th Conference University of Isfahan  January 13, 2020 
Title:
On obstructions to extending group actions to bordisms
Speaker:
Sam Nariman, Copenhagen/Purdue University
Date, Time, and Venue: Thursday, January 2  11:4512:30  Hall 1
Abstract:
Motivated by a question of Ghys, we talk about cohomological obstructions to extending group actions on the boundary $\partial M$ of a $3$manifold to a $C^0$action on $M$.
Among other results, we show that for a $3$manifold $M$, the $S^1 \times S^1$ action on the boundary does not extend to a $C^0$action of $S^1 \times S^1$ as a discrete group on $M$, except in the trivial case $M \cong D^2 \times S^1$. Using additional techniques from 3manifold topology, homotopy theory, and lowdimensional dynamics, we find group actions on a torus and a sphere that are not nullbordant, i.e. they admit no extension to an action by diffeomorphisms on any manifold $M$ with $\partial M \cong T^2$ or $S^2$. This is a joint work with K.Mann.
