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- David Coulson, Oliver Goodman, Craig Hodgson, Walter D. Neumann
- Experimental Mathematics
- 2000

This paper describes “Snap”, a computer program for computing arithmetic invariants of hyperbolic 3-manifolds. Snap is based on Jeff Weeks’s program “SnapPea” [41] and the number theory package “Pari” [5]. SnapPea computes the hyperbolic structure on a finite volume hyperbolic 3-manifold numerically (from its topology) and uses it to compute much geometric… (More)

- Craig Hodgson, Jeffrey R. Weeks
- Experimental Mathematics
- 1994

Hodgson was partially supported by the Australian Research Council. Weeks was partially supported by the National Science Foundation grant DMS-8920161, through the Geometry Center at the University of Minnesota.

- 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)

- Oliver Goodman, Damian Heard, Craig Hodgson
- Experimental Mathematics
- 2008

This paper describes a general algorithm for finding the commensurator 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 decompositions. For example, we use this to find the commensurators of all… (More)

- ANDREW COTTON, DAVID FREEMAN, +11 authors Michael Hutchings
- 2005

We characterize least-perimeter enclosures of prescribed area on some piecewise smooth manifolds, including certain polyhedra, double spherical caps, and cylindrical cans. 2000 Mathematics subject classification: primary 49Q10, 53A10.

We describe a characterization of convex polyhedra in H3 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 E3 all of whose vertices lie on the unit sphere. That resolves a problem posed by… (More)

- Craig Hodgson, Richard Akenhead, Kevin Thomas
- Human movement science
- 2014

We aimed to quantify the time-motion characteristics and technical demands of small-sided soccer games (SSGs) played on small, medium and large pitches using a high frequency non-differential global positioning system (NdGPS) that allowed assessment of acceleration and deceleration patterns. Eight male soccer players competed in SSGs comprising 4×4min… (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 topological 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, J HYAM RUBINSTEIN, +5 authors Stephan Tillmann
- 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 a… (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 R0 = arctanh(1/ √ 3) ≈ 0.65848 around the singular set of hyperbolic cone manifolds, removing the previous restrictions on cone angles. We then apply… (More)