Spherical Structures on $(p, q)$ Torus Knots

A. A. Kolpakov

Novosibirsk State University, Mechanics and Mathematics Department

Abstract: A family of cone-manifolds with spherical metric of $(p, q)$ torus knot type singularity was investigated. In case $p$ and $q$ are coprime one obtains a knot and otherwise one obtains a link with $\gcd(p, q)$ components. The domains of existence for spherical cone-metric wereobtained in terms of cone-angles and the analytical volume formulas were derived.

Keywords: spherical geometry, cone-manifolds, torus knots and links.

UDC: 514.135

Received: 12.11.2008