Coarse and synthetic Weil-Petersson geometry: quasi-flats, geodesics, and relative hyperbolicity - Mathematics > Geometric TopologyReportar como inadecuado




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Abstract: We analyze the coarse geometry of the Weil-Petersson metric on Teichm\-ullerspace, focusing on applications to its synthetic geometry in particular thebehavior of geodesics. We settle the question of the strong relativehyperbolicity of the Weil-Petersson metric via consideration of its coarsequasi-isometric model, the -pants graph.- We show that in dimension~3 the pantsgraph is strongly relatively hyperbolic with respect to naturally definedproduct regions and show any quasi-flat lies a bounded distance from a singleproduct. For all higher dimensions there is no non-trivial collection ofsubsets with respect to which it strongly relatively hyperbolic; this extends atheorem of BDM in dimension 6 and higher into the intermediate range it ishyperbolic if and only if the dimension is 1 or 2 BF. Stability and relativestability of quasi-geodesics in dimensions up through 3 provide for a strongunderstanding of the behavior of geodesics and a complete description of theCAT0-boundary of the Weil-Petersson metric via curve-hierarchies and theirassociated -boundary laminations.-



Autor: Jeffrey Brock, Howard Masur

Fuente: https://arxiv.org/







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