Craig Hodgson

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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)
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)
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)
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)
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)
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)
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)
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)