Kleinian Groups and Hyperbolic 3-Manifolds: On hyperbolic and spherical volumes for knot and link cone-manifolds
Kleinian Groups and Hyperbolic 3-Manifolds: On hyperbolic and spherical volumes for knot and link cone-manifolds
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克莱因群和双曲 3 流形：关于结和连接锥流形的双曲和球体积
DOI：
10.1017/cbo9780511542817.008
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
A. Mednykh
中科院分区：
文献类型：
--
作者：
A. Mednykh
本文把环和纽结看作是以三球面为底空间的几何锥流形的奇异子集。得到了8字形纽结、Whitehead环和Borromean环的奇异分支长度与锥角之间的三角恒等式。这给出了用锥角表示长度的可能性。然后Schläfli公式适用于找到明确的公式双曲和球形体积的这些锥流形。
In the present paper links and knots are considered as singular subsets of geometric cone–manifolds with the three-sphere as an underlying space. Trigonometrical identities between lengths of singular components and cone angles for the figure eight knot, Whitehead link and Borromean rings are obtained. This gives a possibility to express the lengths in terms of cone angles. Then the Schläfli formula applies to find explicit formulae for hyperbolic and spherical volumes of these cone-manifolds.