Global fixed points for centralizers and Morita's theorem

John Franks*, Michael Handel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We prove a global fixed point theorem for the centralizer of a homeomorphism of the two-dimensional disk D that has attractor-repeller dynamics on the boundary with at least two attractors and two repellers. As one application we give an elementary proof of Morita's Theorem, that the mapping class group of a closed surface S of genus g does not lift to the group of C2 diffeomorphisms of S and we improve the lower bound for g from 5 to 3.

Original languageEnglish (US)
Pages (from-to)87-98
Number of pages12
JournalGeometry and Topology
Issue number1
StatePublished - 2009


  • Global fixed point
  • Lifting problem
  • Mapping class group
  • Pseudo-anosov

ASJC Scopus subject areas

  • Geometry and Topology

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