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- W2187446913 abstract "Using the geometric model of the pants complex, we study the Asymptotic Cone of Teichmuller space equipped with the Weil- Petersson metric, for all surfaces S of nite type. In particular, we provide a characterization of the canonical nest pieces in tree-graded structure of the asymptotic cone along the same lines as a similar charac- terization for the mapping class group in (BKMM) and for right angled Artin groups in (BC). As a corollary of the characterization, we com- plete the thickness classication of Teichmuller spaces for all surfaces of nite type, thereby answering questions of Behrstock-Drut u-Mosher (BDM), Brock-Masur (BM), and Behrstock-Drut u (BD). In particu- lar, we prove that Teichmuller space of the genus two surface with one boundary component (or equivalently puncture) can be uniquely char- acterized in the following two senses: it is thick of order two, and it has superquadratic yet subexponential divergence. As a tool in the paper, we develop a natural relative of the curve complex called the complex of separating multicurves, S(S); a -hyperbolic combinatorial complex which encodes the rich interlocking network of natural quasi- convex product regions in Teichmuller space, and may be of independent interest." @default.
- W2187446913 created "2016-06-24" @default.
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- W2187446913 date "2011-01-01" @default.
- W2187446913 modified "2023-09-27" @default.
- W2187446913 title "THE ASYMPTOTIC CONE OF TEICHM ULLER SPACE: TREE-GRADED STRUCTURE AND DIVERGENCE" @default.
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