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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)

INTRODUCTION
Colo-vesical (CV) fistulae are the most common type of fistulae associated with diverticular disease. Surgery remains the mainstay of treatment, without which, CV fistulae rarely achieve complete healing.
PRESENTATION OF CASE
Herein, we report the case of a 62-year-old man who developed a CV fistula after reversal of Hartmann's procedure… (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)

- Ahmad Issa, Craig Hodgson
- 2012

Acknowledgements Firstly, I'd like to express my gratitude to Craig; I feel privileged to have had such an excellent supervisor who was generous with his time and ideas, and who helped me grow throughout the course of this project. I'd also like to thank Henry Segerman who contributed substantially to this thesis in various forms, in particular for the many… (More)

In this paper we enumerate and classify the " simplest " pairs (M, G) where M is a closed orientable 3-manifold and G is a trivalent graph embedded in M. To enumerate the pairs we use a variation of Matveev's definition of complexity for 3-manifolds, and we consider only (0, 1, 2)-irreducible pairs, namely pairs (M, G) such that any 2-sphere in M… (More)

- James Saunderson, Craig Hodgson
- 2008

Mostow's Rigidity Theorem is a stunning bridge between the worlds of geometry and topology. It tells us that the geometry of closed hyperbolic n-manifolds, for n ≥ 3, is completely determined by their fundamental groups. The proofs of this result are many and varied — all of them substantial and involving machinery from a number of areas of mathematics. The… (More)

- Nick Sheridan, Craig Hodgson, Hyam Rubinstein
- 2008

The aim of this project is to introduce the basics of Hamilton's Ricci Flow. The Ricci flow is a pde for evolving the metric tensor in a Riemannian manifold to make it " rounder " , in the hope that one may draw topological conclusions from the existence of such " round " metrics. Indeed, the Ricci flow has recently been used to prove two very deep theorems… (More)

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