Large-scale Rank and Rigidity of the Weil-petersson Metric
نویسنده
چکیده
We study the large-scale geometry of Weil-Petersson space, that is, Teichmüller space equipped with the Weil-Petersson metric. We show that this admits a natural coarse median structure of a specific rank. Given that this is equal to the maximal dimension of a quasi-isometrically embedded euclidean space, we recover a result of Eskin Masur and Rafi which gives the coarse rank of the space. We go on to show that, apart from finitely many cases, the Weil-Petersson spaces are quasi-isometrically distinct, and quasi-isometrically rigid. By a theorem of Brock, WeilPetersson space is quasi-isometric to the pants graph, so our results apply equally well to that space.
منابع مشابه
Rank and Rigidity Properties of Spaces Associated to a Surface
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