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We calculate the Chern-Simons invariants of the hyperbolic double twist knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of cone-manifold structures of double twist knots.

We calculate the Chern-Simons invariants of the hyperbolic double twist knot orbifolds using the Schläfli formula for the generalized ChernSimons function on the family of cone-manifold structures of double twist knots. [ABSTRACT FROM AUTHOR]

We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation C(2 n, 3) using the Schläfli formula for the generalized Chern-Simons function on the family of C(2 n, 3) cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham and Lee's methods. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic C(2 n, 3) orbifolds. [ABSTRACT FROM AUTHOR]

Let be the family of two bridge knots of slope . We calculate the volumes of the 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 , 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. [ABSTRACT FROM AUTHOR]

We calculate the volumes of the hyperbolic twist knot cone-manifolds using the Schläfli formula. Even though general ideas for calculating the volumes of cone-manifolds are around, since there is no concrete calculation written, we present here the concrete calculations. We express the length of the singular locus in terms of the distance between the two axes fixed by two generators. In this way the calculation becomes easier than using the singular locus directly. The volumes of the hyperbolic twist knot cone-manifolds simpler than Stevedore's knot are known. As an application, we give the volumes of the cyclic coverings over the hyperbolic twist knots. [ABSTRACT FROM AUTHOR]