Communications in Analysis and Geometry

Volume 22 (2014)

Number 5

Exact volume of hyperbolic 2-bridge links

Pages: 881 – 896

DOI: http://dx.doi.org/10.4310/CAG.2014.v22.n5.a5

Author

Anastasiia Tsvietkova (Department of Mathematics, University of California at Davis)

Abstract

W. Thurston suggested a method for computing hyperbolic volume of hyperbolic 3-manifolds, based on a triangulation of the manifold. The method was implemented by J. Weeks in the program SnapPea, which produces a decimal approximation as a result. For hyperbolic 2-bridge links, we give formulae that allow one to find the exact volume, i.e., to construct a polynomial and to find volume as an analytic function of one of its roots. The computation is performed directly from a reduced, alternating link diagram.

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