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This paper gives a quantitative version of Thurston's hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of non-hyperbolic Dehn fillings on a cusped hyperbolic 3-manifold, and estimates on the changes in volume and core geodesic length during hyperbolic Dehn filling. The proofs involve the construction of a family(More)
1. Introduction This paper describes \Snap", a computer program for computing arithmetic in-variants of hyperbolic 3-manifolds. Snap is based on Jee Weeks's program \Snap-Pea" ?] and the number theory package \Pari" ?]. SnapPea computes the hy-perbolic structure on a nite volume hyperbolic 3-manifold numerically (from its topology) and uses it to compute(More)
This paper describes a general algorithm for finding the commen-surator of a non-arithmetic hyperbolic manifold with cusps, and for deciding when two such manifolds are commensurable. The method is based on some elementary observations regarding horosphere packings and canonical cell de-compositions. For example, we use this to find the commensurators of(More)
This paper concerns the Dehn surgery construction, especially those Dehn surgeries leaving the manifold unchanged. In particular, we describe an oriented 1–cusped hyperbolic 3–manifold X with a pair of slopes r 1 , r 2 such that the Dehn filled manifolds X(r 1), X(r 2) are oppositely oriented copies of the lens space L(49, 18), and there is no homeomorphism(More)
We describe a characterization of convex polyhedra in H 3 in terms of their dihedral angles, developed by Rivin. We also describe some geometric and combinatorial consequences of that theory. One of these consequences is a combinatorial characterization of convex polyhedra in E 3 all of whose vertices lie on the unit sphere. That resolves a problem posed by(More)
This paper gives an exposition of the authors' harmonic deformation theory for 3-dimensional hyperbolic cone-manifolds. We discuss topo-logical applications to hyperbolic Dehn surgery as well as recent applications to Kleinian group theory. A central idea is that local rigidity results (for deformations fixing cone angles) can be turned into effective(More)
In this paper we develop a new theory of infinitesimal harmonic deformations for compact hyperbolic 3-manifolds with " tubular boundary ". In particular, this applies to complements of tubes of radius at least R 0 = arctanh(1/ √ 3) ≈ 0.65848 around the singular set of hyperbolic cone manifolds, removing the previous restrictions on cone angles. We then(More)
Agol recently introduced the concept of a veering taut triangulation of a 3–manifold, which is a taut ideal triangulation with some extra combinatorial structure. We define the weaker notion of a " veering triangulation " and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, giving an example of(More)