Volumes for twist link cone-manifolds

Dmitriy Derevnin; Alexander Mednykh; Michele Mulazzani

Volumes for twist link cone-manifolds

Geometric Topology 2007-05-23 v2

Authors: Dmitriy Derevnin , Alexander Mednykh , Michele Mulazzani

Abstract

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 $6^2_3$ .

Keywords

hyperbolic 3-manifolds hyperbolic geometry simplicial volume

Cite

@article{arxiv.math/0307193,
  title  = {Volumes for twist link cone-manifolds},
  author = {Dmitriy Derevnin and Alexander Mednykh and Michele Mulazzani},
  journal= {arXiv preprint arXiv:math/0307193},
  year   = {2007}
}

Comments

23 pages, 1 figure. Revised version with minor changes. Accepted for publication in the Boletin de la Sociedad Matematica Mexicana, special issue in honor of Francisco "FICO" Gonzales Acuna

Volumes for twist link cone-manifolds

Abstract

Keywords

Cite

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