EVENT DETAILS AND ABSTRACT

Title: Some subgroups of the group of analytic symplectic diffeomorphisms of $S^2$ which are virtually abelian
Speaker: John Franks
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

We show that if $M$ is a compact oriented surface of genus $0$ and $G$ is a subgroup of $\Symp^\omega_\mu(M)$ which has an infinite normal solvable subgroup, then $G$ is virtually abelian. In particular the centralizer $\Cent(f)$ of an infinite order $f \in \Symp^\omega_\mu(M)$ is virtually abelian. Another immediate corollary is that if $G$ is a solvable subgroup of $\Symp^\omega_\mu(M)$ then $G$ is virtually abelian.