Groups, Geometry, and Dynamics

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Volume 6, Issue 2, 2012, pp. 249–278
DOI: 10.4171/GGD/157

Published online: 2012-04-16

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

Matt T. Clay[1], Christopher J. Leininger[2] and Johanna Mangahas[3]

(1) Allegheny College, Meadville, United States
(2) University of Illinois at Urbana-Champaign, USA
(3) Brown University, Providence, USA

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.

Keywords: Right-angled Artin groups, mapping class groups, pseudo-Anosov, Teichmüller space, surface subgroups

Clay Matt, Leininger Christopher, Mangahas Johanna: The geometry of right-angled Artin subgroups of mapping class groups. Groups Geom. Dyn. 6 (2012), 249-278. doi: 10.4171/GGD/157