Volumes for twist link cone-manifolds

2003/07/14 by Dmitriy Derevnin, Alexander Mednykh, Derevnin, Dmitriy +3
Mathematics · #57M25 #57M50 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0307193

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

openalex publication_date 2003/07/14 · arxiv created 2004/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the 3-sphere and the singular set is the knot 4₁ and the links 5²₁ and 6²₂, 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 6²₃ 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 5²₁ and 6²₃.

Related

• Trigonometric identities and volumes of the hyperbolic twist knot cone-manifolds
• Exact integral formulas for volumes of two-bridge knot cone-manifolds
• Volumes of double twist knot cone-manifolds
• On the volume of double twist link cone-manifolds
• Euclidean volumes of hyperbolic knots