arXiv (Cornell University)
The Burnside problem for $\text{Diff}_{\text{Vol}}(\mathbb{S}^2)$
July 2016 • Sebastián Hurtado, Alejandro Kocsard, Federico Rodríguez-Hertz
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.