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Fixed points of abelian actions on S2

Published online by Cambridge University Press:  01 October 2007

JOHN FRANKS,
MICHAEL HANDEL and
KAMLESH PARWANI
JOHN FRANKS
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, USA (email: john@math.northwestern.edu)
MICHAEL HANDEL
Affiliation:
Department of Mathematics and Computer Science, Herbert H Lehman College (CUNY), 250, Bedford Park, Boulevard West, Bronx, NY 10468, USA (email: michael.handel@lehman.cuny.edu)
KAMLESH PARWANI
Affiliation:
Department of Mathematics, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920-3099, USA (email: forty2@math.northwestern.edu)
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Abstract

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We prove that if ${\mathcal F}$ is a finitely generated abelian group of orientation preserving C1 diffeomorphisms of $\mathbb {R}^2$ which leaves invariant a compact set then there is a common fixed point for all elements of ${\mathcal F}$. We also show that if ${\mathcal F}$ 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 ${\mathcal F}$ with index at most two.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 5 , October 2007, pp. 1557 - 1581
Copyright
Copyright © Cambridge University Press 2007

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