Geodesic
The geometry of right-angled Artin subgroups of mapping class groups
Matt T. Clay1 ; Christopher J. Leininger2 orcid ; Johanna Mangahas3
1Allegheny College, Meadville, United States
2University of Illinois at Urbana-Champaign, USA
3Brown University, Providence, USA
Groups, geometry, and dynamics, Tome 6 (2012) no. 2, pp. 249-278

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DOI

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.
DOI : 10.4171/ggd/157
Classification : 57-XX, 20-XX, 00-XX
Mots-clés : Right-angled Artin groups, mapping class groups, pseudo-Anosov, Teichmüller space, surface subgroups

Matt T. Clay  1   ; Christopher J. Leininger  2   ; Johanna Mangahas  3

1 Allegheny College, Meadville, United States
2 University of Illinois at Urbana-Champaign, USA
3 Brown University, Providence, USA 
Matt T. Clay; Christopher J. Leininger; Johanna Mangahas. The geometry of right-angled Artin subgroups  of mapping class groups. Groups, geometry, and dynamics, Tome 6 (2012) no. 2, pp. 249-278. doi: 10.4171/ggd/157
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     title = {The geometry of right-angled {Artin} subgroups  of mapping class groups},
     journal = {Groups, geometry, and dynamics},
     pages = {249--278},
     year = {2012},
     volume = {6},
     number = {2},
     doi = {10.4171/ggd/157},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/157/}
}
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