The geometry of right angled Artin subgroups of mapping class groups

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

2010-07-07

arxiv.org/abs/1007.1129v2

Mathematics

Geometric Topology

26 pages, 6 figures; v2: added references

Scientific paper

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 Teichmuller 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 Teichmuller space.

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