Fixed points of abelian actions on S2

John Franks*, Michael Handel, Kamlesh Parwani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 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 languageEnglish (US)
Pages (from-to)1557-1581
Number of pages25
JournalErgodic Theory and Dynamical Systems
Volume27
Issue number5
DOIs
StatePublished - Oct 2007

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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