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Graphs on surfaces and curves over number fields
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Volumes of two-bridge knots in spaces of constant curvature A. D. Mednykh Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk |
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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. 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 formulas for volume of the corresponding manifold modeled in the hyperbolic, spherical and Euclidean geometries. Language: English |
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