Spherical structures on torus knots and links

TL;DR

This paper investigates spherical cone-manifold structures on torus knots and links, determining their existence domains and providing volume formulas for these geometric configurations.

Contribution

It introduces new existence criteria and volume formulas for spherical structures on specific families of torus knots and links.

Findings

Existence domains for spherical metrics are characterized.

Explicit volume formulas are derived.

Results apply to families of torus knots and links.

Abstract

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.