EVENT DETAILS AND ABSTRACT

Title: Groups of polynomial growth and 1D dynamics
Speaker: Kiran Parkhe
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Abstract:

Let $M$ be a connected one-manifold, and $G$ a group of homeomorphisms of $M$ which is finitely-generated and virtually nilpotent, i.e., which has polynomial growth. We prove a structure theorem which says, roughly, that the manifold decomposes into wandering regions (in which no $G$-orbit is dense), and minimal regions (in which every $G$-orbit is dense); and on the latter, the action is actually abelian.

As a corollary, if $G$ is a group of polynomial growth of degree $d$, then for any $\alpha < 1/d$, any continuous $G$-action on $M$ is conjugate to an action by $C^{1 + \alpha}$ diffeomorphisms. This strengthens a result of Farb and Franks.