Hyperbolic Volumes of Two Bridge Cone-Manifolds

Hyperbolic Volumes of Two Bridge Cone-Manifolds

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In this paper we investigate the existence of hyperbolic, Euclidean and spherical structures on cone-manifolds with underlying space 3-sphere and Strategie di spazializzazione dei contenuti nel GeniusLoci Digitale with singular set a given two-bridge knot.For two-bridge knots with 8 crossings we present trigonometric identities involving the length of singular geodesics and cone angles of OCTOPUS: operation control system for task optimization and job parallelization via a user-optimal scheduler such cone-manifolds.Then these identities are used to produce exact integral formulae for the volume of the corresponding cone-manifold modeled in the hyperbolic space.