Some virtually abelian subgroups of the group of analytic symplectic diffeomorphisms of a surface

John M Franks, Michael Handel

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We show that if M is a compact oriented surface of genus 0 and G is a subgroup of Sympωμ (M) that has an infinite normal solvable subgroup, then G is virtually abelian. In particular the centralizer of an infinite order f ∈ Sympωμ(M) is virtually abelian. Another immediate corollary is that if G is a solvable subgroup of Sympωμ(M) then G is virtually abelian. We also prove a special case of the Tits Alternative for subgroups of Sympωμ(M).

Original languageEnglish (US)
Pages (from-to)369-394
Number of pages26
JournalJournal of Modern Dynamics
Volume7
Issue number3
DOIs
StatePublished - Dec 24 2013

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Diffeomorphisms
Subgroup
Centralizer
Genus
Corollary
Alternatives

Keywords

  • Area-preserving
  • Entropy
  • Surface diffeomorphism groups

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Cite this

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Some virtually abelian subgroups of the group of analytic symplectic diffeomorphisms of a surface. / Franks, John M; Handel, Michael.

In: Journal of Modern Dynamics, Vol. 7, No. 3, 24.12.2013, p. 369-394.

Research output: Contribution to journalArticle

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