The volume of hyperbolic cone-manifolds of the knot with Conway's notation $C(2n,3)$

Abstract

Let $C(2n,3)$ be the family of two bridge knots of slope $(4n+1)/(6n+1)$. We calculate the volumes of the $C(2n,3)$ cone-manifolds using the Schläfli formula. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham, Mednykh, and Petrov's methods. As an application, we give the volumes of the cyclic coverings over those knots. For the fundamental group of $C(2n,3)$, we take and tailor Hoste and Shanahan's. As a byproduct, we give an affirmative answer for their question whether their presentation is actually derived from Schubert's canonical 2-bridge diagram or not.

10 pages, 3 figures. To appear in Journal of knot theory and its ramifications. arXiv admin note: text overlap with arXiv:1403.1941

References in corpus (2)

• Deforming Euclidean cone 3-manifolds
• Volumes for twist link cone-manifolds

Cited by in corpus (1)

• Rolling Skyrmions and the Nuclear Spin-Orbit Force