Bounded combinatorics and uniform models for hyperbolic 3-manifolds

Jeffrey Brock; Yair Minsky; Hossein Namazi; Juan Souto

doi:10.1112/jtopol/jtv043

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arXiv · 1312.2293

Bounded combinatorics and uniform models for hyperbolic 3-manifolds

Jeffrey Brock·Yair Minsky·Hossein Namazi·Juan Souto

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Abstract

Bounded-type 3-manifolds arise as combinatorially bounded gluings of irreducible 3-manifolds chosen from a finite list. We prove effective hyperbolization and effective rigidity for a broad class of 3-manifolds of bounded type and large gluing heights. Specifically, we show the existence and uniqueness of hyperbolic metrics on 3-manifolds of bounded type and large heights, and prove existence of a bilipschitz diffeomorphism to a combinatorial model described explicitly in terms of the list of irreducible manifolds, the topology of the identification, and the combinatorics of the gluing maps.

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Jeffrey Brock, Yair Minsky, Hossein Namazi, Juan Souto. 2013-12-09. Bounded combinatorics and uniform models for hyperbolic 3-manifolds. https://doi.org/10.1112/jtopol%2Fjtv043

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