Computation of Hyperbolic Structures in Knot Theory

Details Computation of Hyperbolic Structures in Knot Theory Computation of Hyperbolic Structures in Knot Theory

2003-09-24

arxiv.org/abs/math/0309407v1

Mathematics

Geometric Topology

To appear in the Handbook of Knot Theory. 26 pages, 22 figures

Scientific paper

This chapter from the upcoming Handbook of Knot Theory (eds. Menasco and Thistlethwaite) shows how to construct hyperbolic structures on link complements and perform hyperbolic Dehn filling. Along with a new elementary exposition of the standard ideas from Thurston's work, the article includes never-before-published explanations of SnapPea's algorithms for triangulating a link complement efficiently and for converging quickly to the hyperbolic structure while avoiding singularities in the parameter space.

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