Fixed Points of abelian actions on S2
John Franks, Michael Handel, Kamlesh Parwani
Abstract
We prove that if F is a finitely generated abelian group of orientation preserving C1 diffeomorphisms of R2 which leaves invariant a compact set then there is a common fixed point for all elements of F. We also show that if F is any abelian subgroup of orientation preserving C1 diffeomorphisms of S2 then there is a common fixed point for all elements of a subgroup of F with index at most two.
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