Geodesic
Hyperbolic volumes of two bridge cone-manifolds
The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 21-33

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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 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 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.
Keywords: cone-manifold, orbifold, two-bridge knot, geodesic length.
Mots-clés : volume 
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A. D. Mednykh; A. B. Qutbaev. Hyperbolic volumes of two bridge cone-manifolds. The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 21-33. http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a1/