Document Type
Article
Publication Date
October 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.
Recommended Citation
Franks, John; Handel, Michael; and Parwani, Kamlesh, "Fixed points of abelian actions on S2" (2007). Faculty Research and Creative Activity. 23.
https://thekeep.eiu.edu/math_fac/23
https://works.bepress.com/kamlesh_parwani/6/
