2003/09/24 by Jeffrey R. Weeks, Weeks, Jeffrey R.
Mathematics · #57M25 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57M50
paper · pdf · doi:10.48550/arxiv.math/0309407
To appear in the Handbook of Knot Theory. 26 pages, 22 figures
arxiv created 2003/09/24 · arxiv updated 2009/12/01
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.