Hyperbolic Volumes of Two Bridge Cone-Manifolds

被引：0

作者：

Mednykh, Alexander D. ^{[1
,2
]}

Qutbaev, Aydos B. ^{[1
,2
,3
]}

机构：

[1] RAS, Sobolev Inst Math SB, Novosibirsk, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Nukus State Pedag Inst, Nukus, Karakalpakstan, Uzbekistan

来源：

BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS | 2025年 / 51卷

关键词：

cone-manifold; orbifold; two-bridge knot; volume; geodesic length; PERSONAL ACCOUNT; DISCOVERY;

D O I：

10.26516/1997-7670.2025.51.21

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：21 / 33

页数：13

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