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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)

- 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)

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)

- 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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