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Volumes of two-bridge cone manifolds in spaces of constant curvature. / Mednykh, A. D.

In: Transformation Groups, Vol. 26, No. 2, 06.2021, p. 601-629.

Research output: Contribution to journal › Article › peer-review

Harvard

Mednykh, AD 2021, 'Volumes of two-bridge cone manifolds in spaces of constant curvature', Transformation Groups, vol. 26, no. 2, pp. 601-629. https://doi.org/10.1007/s00031-020-09632-x

APA

Mednykh, A. D. (2021). Volumes of two-bridge cone manifolds in spaces of constant curvature. Transformation Groups, 26(2), 601-629. https://doi.org/10.1007/s00031-020-09632-x

Vancouver

Mednykh AD. Volumes of two-bridge cone manifolds in spaces of constant curvature. Transformation Groups. 2021 Jun;26(2):601-629. Epub 2020 Nov 24. doi: 10.1007/s00031-020-09632-x

Author

Mednykh, A. D. / Volumes of two-bridge cone manifolds in spaces of constant curvature. In: Transformation Groups. 2021 ; Vol. 26, No. 2. pp. 601-629.

BibTeX

@article{86bc994faece4445acac0ad4058c9a14,
title = "Volumes of two-bridge cone manifolds in spaces of constant curvature",
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. 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.",
keywords = "HYPERBOLIC STRUCTURES, PERSONAL ACCOUNT, KNOTS, 3-MANIFOLDS, INVARIANTS, DISCOVERY, COVERINGS",
author = "Mednykh, {A. D.}",
note = "Funding Information: The research was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (Contract No. 14.Y26.31.0025). Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2021",
month = jun,
doi = "10.1007/s00031-020-09632-x",
language = "English",
volume = "26",
pages = "601--629",
journal = "Transformation Groups",
issn = "1083-4362",
publisher = "Birkhauser Boston",
number = "2",

}

RIS

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 -

ID: 26140330