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VOLUMES OF TWO-BRIDGE CONE MANIFOLDS IN SPACES OF CONSTANT CURVATURE

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Abstract

We investigate the existence of hyperbolic, spherical or Euclidean structure on cone-manifolds whose underlying space is the three-dimensional sphere and singular set is a given two-bridge knot. For two-bridge knots with not more than 7 crossings we present trigonometrical identities involving the lengths of singular geodesics and cone angles of 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, spherical and Euclidean geometries.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Koptuga, 4, 630090, Novosibirsk, Russia

    A. D. MEDNYKH

  2. Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia

    A. D. MEDNYKH

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Devoted to the memory of Ernest Borisovich Vinberg who was a true Man, Teacher and Mathematician

The research was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (Contract No. 14.Y26.31.0025).

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MEDNYKH, A.D. VOLUMES OF TWO-BRIDGE CONE MANIFOLDS IN SPACES OF CONSTANT CURVATURE. Transformation Groups 26, 601–629 (2021). https://doi.org/10.1007/s00031-020-09632-x

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