Article
Fixed points of abelian actions on S2
Ergodic Theory and Dynamical Systems
(2007)
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.
Disciplines
Publication Date
October, 2007
Citation Information
John Franks, Michael Handel and Kamlesh Parwani. "Fixed points of abelian actions on S2" Ergodic Theory and Dynamical Systems Vol. 27 Iss. 5 (2007) Available at: http://works.bepress.com/kamlesh_parwani/6/