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Computation of Hyperbolic Structures in Knot Theory

Jeffrey R. Weeks
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Abstract

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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Jeffrey R. Weeks. 2003-09-24. Computation of Hyperbolic Structures in Knot Theory. https://arxiv.org/abs/math/0309407

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