TY - JOUR

T1 - Hyperbolic Volumes of Two Bridge Cone-Manifolds

AU - Mednykh, Alexander D.

AU - Qutbaev, Aydos B.

N1 - Mednykh A. D., Qutbaev A. B. Hyperbolic Volumes of Two Bridge ConeManifolds. / A. D. Mednykh, A. B. Qutbaev // The Bulletin of Irkutsk State University. Series Mathematics. - 2025. - 51. - C. 21–33. - doi: 10.26516/1997-7670.2025.51.21

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - cone-manifold

KW - geodesic length

KW - orbifold

KW - two-bridge knot

KW - volume

UR - https://www.mendeley.com/catalogue/69986a83-e2e8-3ae9-8931-731c799cbffe/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105000872980&origin=inward&txGid=b074a3ee199e2aecd7fa618fe501a74b

UR - https://elibrary.ru/item.asp?id=80370956

U2 - 10.26516/1997-7670.2025.51.21

DO - 10.26516/1997-7670.2025.51.21

M3 - Article

VL - 51

SP - 21

EP - 33

JO - Bulletin of Irkutsk State University, Series Mathematics

JF - Bulletin of Irkutsk State University, Series Mathematics

SN - 1997-7670

ER -