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

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 surfaces (for any at least 2) in the moduli space of genus surfaces (for any 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