Fixed points of abelian actions on S2

John Franks; Michael Handel; Kamlesh Parwani

doi:10.1017/S0143385706001088

Fixed points of abelian actions on S²

John Franks^*, Michael Handel, Kamlesh Parwani

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1557-1581
Number of pages	25
Journal	Ergodic Theory and Dynamical Systems
Volume	27
Issue number	5
DOIs	https://doi.org/10.1017/S0143385706001088
State	Published - Oct 2007

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/S0143385706001088

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title = "Fixed points of abelian actions on S2",

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.",

author = "John Franks and Michael Handel and Kamlesh Parwani",

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N2 - 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.

AB - 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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Fixed points of abelian actions on S²

Abstract

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