Volumes for twist link cone-manifolds

Details Volumes for twist link cone-manifolds Volumes for twist link cone-manifolds

2003-07-14

arxiv.org/abs/math/0307193v2

Mathematics

Geometric Topology

23 pages, 1 figure. Revised version with minor changes. Accepted for publication in the Boletin de la Sociedad Matematica Mexi

Scientific paper

Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the 3-sphere and the singular set is the knot $4_1$ and the links $5^2_1$ and $6^2_2$, have been obtained by the second named author and his collaborators. In this paper we explicitly find the hyperbolic volume for cone-manifolds with the link $6^2_3$ as singular set. Trigonometric identities (Tangent, Sine and Cosine Rules) between complex lengths of singular components and cone angles are obtained for an infinite family of two-bridge links containing $5^2_1$ and $6^2_3$.

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