# Algebra/Topology Seminar

Sam Nariman (Northwestern University / UCHP)

Title: On obstructions to extending group actions to bordisms

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 3-manifold topology, homotopy theory, and low-dimensional 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.