Bounded combinatorics and uniform models for hyperbolic 3-manifolds
Geometric Topology
2017-05-17 v1
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.
Cite
@article{arxiv.1312.2293,
title = {Bounded combinatorics and uniform models for hyperbolic 3-manifolds},
author = {Jeffrey Brock and Yair Minsky and Hossein Namazi and Juan Souto},
journal= {arXiv preprint arXiv:1312.2293},
year = {2017}
}