Area preserving group actions on surfaces

John Franks*, Michael Handel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional integer Heisenberg group. For example any finite index subgroup of SL(3,ℤ) is such a group. The main result of this paper is that every action of G on a closed oriented surface by area preserving diffeomorphisms factors through a finite group.

Original languageEnglish (US)
Pages (from-to)757-771
Number of pages15
JournalGeometry and Topology
StatePublished - 2003


  • Almost simple
  • Group actions
  • Heisenberg group

ASJC Scopus subject areas

  • Geometry and Topology


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