Zero entropy subgroups of mapping class groups

John M Franks, Kamlesh Parwani*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

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
Volume186
Issue number1
DOIs
StatePublished - Feb 1 2017

Fingerprint

Mapping Class Group
Pseudo-Anosov
Entropy
Subgroup
Finite Set
Zero
Permutation group
Invariant Set
Group Action
Permutation

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Franks, John M ; Parwani, Kamlesh. / Zero entropy subgroups of mapping class groups. In: Geometriae Dedicata. 2017 ; Vol. 186, No. 1. pp. 27-38.
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Zero entropy subgroups of mapping class groups. / Franks, John M; Parwani, Kamlesh.

In: Geometriae Dedicata, Vol. 186, No. 1, 01.02.2017, p. 27-38.

Research output: Contribution to journalArticle

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