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

Abstract

Let [Formula: see text] be the family of two bridge knots of slope [Formula: see text]. We calculate the volumes of the [Formula: see text] 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 [Formula: see text], 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 two-bridge diagram or not.