Geometry, Topology and Dynamics Seminar
Michael Hull
UIC
Transitivity degrees of countable groups.
Abstract: We introduce the transitivity degree of a countable group $G$, denoted $td(G)$, as the $\sup$ over all $k$ such that $G$ admits a faithful, $k$-transitive action on an set with at least k elements. We show that for many classes of infinite groups (e.g. hyperbolic groups, mapping class groups, 3-manifold groups, RAAGS, or any infinite subgroups of one of these), $td(G)\in\{1, \infty\}$. In particular, we show that if $G$ is acylindrically hyperbolic and $G$ has no finite normal subgroups, $G$ admits a faithful action which is highly transitive, that is $k$-transitive for all $k$. We will also mention some applications of this result to the universal theory of acylindrically hyperbolic groups.
Monday September 22, 2014 at 3:00 PM in SEO 636