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- CRAIG D. HODGSON
- 2005

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)

- ANDREW COTTON, DAVID FREEMAN, ANDREI GNEPP, TING NG, JOHN SPIVACK, C. D. Hodgson +8 others
- 2005

We characterize least-perimeter enclosures of prescribed area on some piecewise smooth manifolds, including certain polyhedra, double spherical caps, and cylindrical cans.

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)

- Steven A Bleiler, Craig D Hodgson, Jeffrey R Weeks
- 2008

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)

- Craig D Hodgson, Steven P Kerckhoff
- 2003

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)

- CRAIG D. HODGSON, STEVEN P. KERCKHOFF
- 2008

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)

- CRAIG D HODGSON, J HYAM RUBINSTEIN, HENRY SEGERMAN, STEPHAN TILLMANN, Craig D Hodgson, J Hyam Rubinstein +2 others
- 2011

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)