Computation of Hyperbolic Structures in Knot Theory
Jeffrey R. Weeks
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.
Create a lesson
Related papers
Linearity of Graph Manifold Groups
Daniel T. Wise
Finding the Birman-Series set
Peter Buser, Hugo Parlier
Thurston's Legacy at the Interface of Surface Dynamics, Train Tracks, and Arithmetic
Ahmad Rafiqi, Ayberk Zeytin
Recognizing oriented knots from finite quotients with one marked element
Indranil Biswas, Shrinit Singh
Symmetries of colored Khovanov-Rozansky homology
Alexis Guérin, Felix Roz
The Colored Jones Function does not determine any colored Links--Gould polynomial
Matthew Harper, Ben-Michael Kohli