Zero entropy subgroups of mapping class groups

John Franks, Kamlesh Parwani*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a group action on a surface with a finite invariant set we investigate how the algebraic properties of the induced group of permutations of that set affects the dynamical properties of the group. Our main result shows that in many circumstances if the induced permutation group is not solvable then among the homeomorphisms in the group there must be one with a pseudo-Anosov component. We formulate this in terms of the mapping class group relative to the finite set and show the stronger result that in many circumstances (e.g. if the surface has boundary) if this mapping class group has no elements with pseudo-Anosov components then it is itself solvable.

Original languageEnglish (US)
Pages (from-to)27-38
Number of pages12
JournalGeometriae Dedicata
Issue number1
StatePublished - Feb 1 2017


  • Entropy
  • Homeomorphisms and diffeomorphisms of planes and surfaces
  • Mapping class groups

ASJC Scopus subject areas

  • Geometry and Topology


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