Fixed Points of abelian actions on $S^2$

John Franks; Michael Handel; Kamlesh Parwani

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arXiv · math/0509574

Fixed Points of abelian actions on $S^2$

John Franks·Michael Handel·Kamlesh Parwani

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Abstract

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.

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BibTeX RIS

John Franks, Michael Handel, Kamlesh Parwani. 2005-12-29. Fixed Points of abelian actions on $S^2$. https://arxiv.org/abs/math/0509574

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