The geometry of right-angled Artin subgroups of mapping class groups

Matt T. Clay, Christopher J. Leininger, Johanna Mangahas

Research output: Contribution to journalArticlepeer-review

Abstract

We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmüller space is a quasi-isometric embedding for both of the standard metrics. As a consequence, we produce infinitely many genus h surfaces (for any h at least 2) in the moduli space of genus g surfaces (for any g at least 3) for which the universal covers are quasi-isometrically embedded in the Teichmüller space.

Original languageEnglish (US)
Pages (from-to)249-278
Number of pages30
JournalGroups, Geometry, and Dynamics
Volume6
Issue number2
DOIs
StatePublished - 2012

Keywords

  • Mapping class groups
  • Pseudo-Anosov
  • Right-angled Artin groups
  • Surface subgroups
  • Teichmüller space

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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