A. A. Kolpakov, A. D. Mednykh, “Spherical structures on torus knots and links”, Sibirsk. Mat. Zh., 2009, Volume 50, Number 5,Pages <nobr>1083

This article is cited in 7 papers

Spherical structures on torus knots and links

A. A. Kolpakov^a, A. D. Mednykh^b

^a Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We study two infinite families of cone manifolds endowed with a spherical metric. The singular set of the first of them is the torus knot $\mathrm t(2n+1,2)$ and the singular set of the second is the two-component link $\mathrm t(2n,2)$. We find the domains of sphericity of these cone manifolds in terms of cone angles and obtain analytic formulas for their volumes.

Keywords: spherical geometry, cone manifold, knot, link.

UDC: 514.135

Received: 02.05.2008
Revised: 05.12.2008