TY - JOUR

T1 - Volumes of two-bridge cone manifolds in spaces of constant curvature

AU - Mednykh, A. D.

N1 - Funding Information: The research was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (Contract No. 14.Y26.31.0025). Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2021/6

Y1 - 2021/6

N2 - 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.

AB - 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.

KW - HYPERBOLIC STRUCTURES

KW - PERSONAL ACCOUNT

KW - KNOTS

KW - 3-MANIFOLDS

KW - INVARIANTS

KW - DISCOVERY

KW - COVERINGS

UR - http://www.scopus.com/inward/record.url?scp=85096541189&partnerID=8YFLogxK

U2 - 10.1007/s00031-020-09632-x

DO - 10.1007/s00031-020-09632-x

M3 - Article

AN - SCOPUS:85096541189

VL - 26

SP - 601

EP - 629

JO - Transformation Groups

JF - Transformation Groups

SN - 1083-4362

IS - 2

ER -