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 Schlafli 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 two-bridge diagram or not.