JournalsggdVol. 6, No. 2pp. 249–278

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

  • Matt T. Clay

    Allegheny College, Meadville, United States
  • Christopher J. Leininger

    University of Illinois at Urbana-Champaign, USA
  • Johanna Mangahas

    Brown University, Providence, USA
The geometry of right-angled Artin subgroups  of mapping class groups cover
Download PDF

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 hh surfaces (for any hh at least 2) in the moduli space of genus gg surfaces (for any gg at least 3) for which the universal covers are quasi-isometrically embedded in the Teichmüller space.

Cite this article

Matt T. Clay, Christopher J. Leininger, Johanna Mangahas, The geometry of right-angled Artin subgroups of mapping class groups. Groups Geom. Dyn. 6 (2012), no. 2, pp. 249–278

DOI 10.4171/GGD/157