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Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani
Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani
Kamlesh Parwani
We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ 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 $C^1$ diffeomorphisms of $S^2$ then there is a common fixed point for all elements of a subgroup of $F$ with index at most two.
Fixed Points Of Abelian Actions, John Franks, Michael Handel, Kamlesh Parwani
Fixed Points Of Abelian Actions, John Franks, Michael Handel, Kamlesh Parwani
Kamlesh Parwani
We prove that if $\F$ 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 $\F.$