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Article Dans Une Revue Journal of topology Année : 2016

Bounded combinatorics and uniform models for hyperbolic 3-manifolds

Jeffrey Brock
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Yair Minsky
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Hossein Namazi
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Juan Souto

Résumé

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.

Dates et versions

hal-01343314 , version 1 (08-07-2016)

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Jeffrey Brock, Yair Minsky, Hossein Namazi, Juan Souto. Bounded combinatorics and uniform models for hyperbolic 3-manifolds. Journal of topology, 2016, 9 (2), pp.451-501. ⟨10.1112/jtopol/jtv043⟩. ⟨hal-01343314⟩
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