English

Fixed Points of abelian actions on $S^2$

Dynamical Systems 2007-05-23 v2

Abstract

We prove that if FF is a finitely generated abelian group of orientation preserving C1C^1 diffeomorphisms of R2R^2 which leaves invariant a compact set then there is a common fixed point for all elements of F.F. We also show that if FF is any abelian subgroup of orientation preserving C1C^1 diffeomorphisms of S2S^2 then there is a common fixed point for all elements of a subgroup of FF with index at most two.

Keywords

Cite

@article{arxiv.math/0509574,
  title  = {Fixed Points of abelian actions on $S^2$},
  author = {John Franks and Michael Handel and Kamlesh Parwani},
  journal= {arXiv preprint arXiv:math/0509574},
  year   = {2007}
}
R2 v1 2026-07-22T17:24:58.973Z