Exact volume of hyperbolic 2-bridge links

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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Published 29 October 2014