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Oct 13, 2013 at 18:47 vote accept Anonymous
Oct 13, 2013 at 17:15 answer added Ian Agol timeline score: 5
Oct 13, 2013 at 16:48 comment added Ian Agol Ok, good point Misha! I implicitly assumed he was looking for an equivariant quasi-isometry, so whether the orbit of a point under the mcg is a q.i. embedding.
Oct 13, 2013 at 14:29 comment added Misha @Ian: I am not sure, since a qi embedding might be unrelated to the standard action of the mcg.
Oct 13, 2013 at 4:14 comment added Ian Agol I believe the answer is no for Teichmuller and Weil-Petersson: I think this follows from work of Minsky, Rafi, and Brock, who found combinatorial models for measuring distance in the mapping class group, Teichmuller metric, and Weil-Petersson metric respectively.
Oct 13, 2013 at 3:52 comment added Cusp This is not exactly the answer you want but you can find some related results here <arxiv.org/abs/math/0701719>
Oct 13, 2013 at 3:40 history edited Anonymous
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Oct 13, 2013 at 3:15 history asked Anonymous CC BY-SA 3.0