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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 51

Hyperbolic Volumes of Two Bridge Cone-Manifolds

Author(s)
Alexander D. Mednykh1,2, Aydos B. Qutbaev1,2,3

1Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation

2Novosibirsk State University, Novosibirsk, Russian Federation

3Nukus State Pedagogical Institute named after Ajiniyaz, Nukus, Karakalpakstan, Uzbekistan

Abstract
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.
About the Authors

Alexander D. Mednykh, Dr. Sci. (Phys.-Math.), Prof., Sobolev Institute of Mathematics SB RAS, Novosibirsk, 630090, Russian Federation, Novosibirsk State University, Novosibirsk, 630090, Russian Federation, smedn@mail.ru

Aydos B. Qutbaev, Sobolev Institute of Mathematics SB RAS, Novosibirsk, 630090, Russian Federation, Novosibirsk State University, Novosibirsk, 630090, Russian Federation, aydosqutbaev@gmail.com

For citation

Mednykh A. D., Qutbaev A. B. Hyperbolic Volumes of Two Bridge ConeManifolds. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 51, pp. 21–33.

https://doi.org/10.26516/1997-7670.2025.51.21

Keywords
cone-manifold, orbifold, two-bridge knot, volume, geodesic length
UDC
517.51
MSC
57K32, 57M50
DOI
https://doi.org/10.26516/1997-7670.2025.51.21
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