The geometry of right-angled Artin subgroups of mapping class groups
Matt T. Clay
Allegheny College, Meadville, United StatesChristopher J. Leininger
University of Illinois at Urbana-Champaign, USAJohanna Mangahas
Brown University, Providence, USA
![The geometry of right-angled Artin subgroups of mapping class groups cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-6-issue-2.png&w=3840&q=90)
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