Groups acting distally and minimally on ${\mathbb{S}}^2$ and ${\mathbb{RP}}^2$

Abstract

Let $X$ be the $2$-sphere ${\mathbb{S}}^2$ or the real projective plane ${\mathbb{RP}}^2$. We show that if $\Gamma$ is a finitely generated group acting minimally and distally on $X$, then $\Gamma$ contains a nonabelian free subgroup.