The Burnside problem for ${\text{Diff}}_{\text{Vol}}({\mathbb{S}}^2)$

Abstract

Let $S$ be a closed surface and ${\text{Diff}}_{\text{Vol}}(S)$ be the group of volume preserving diffeomorphisms of $S$. A finitely generated group $G$ is periodic of bounded exponent if there exists $k\in \mathbb{N}$ such that every element of $G$ has order at most $k$. We show that every periodic group of bounded exponent $G\subset {\text{Diff}}_{\text{Vol}}(S)$ is a finite group.

Added Alejandro Kocsard and Federico Rodríguez-Hertz as coauthors. Include new results about actions of periodic groups on Tori and hyperbolic manifolds

References in corpus (3)

• Groups acting on manifolds: around the Zimmer program
• Livsic theorem for diffeomorphism cocycles
• On periodic groups of homeomorphisms of the 2-dimensional sphere