Fixed points of Abelian actions
Fixed points of Abelian actions
We prove that if $\mathfrak{F}$ is an abelian group of $C^1$ diffeomorphisms isotopic to the identity of a closed surface $S$ of genus at least two, then there is a common fixed point for all elements of $\mathfrak{F}$. If $\mathfrak{F}$ is an abelian group of $C^1$ diffeomorphisms (not necessarily isotopic …