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Explicit formulae for Chern-Simons invariants of the hyperbolic knot orbifolds
We calculate the Chern-Simons invariants of the hyperbolic knot
orbifolds using the Schl\"{a}fli formula for the generalized Chern-Simons
function on the family of cone-manifold structures of knot. 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 to a bi-infinite family. We dealt with even slopes just as easily
as odd ones. As an application, we calculate the Chern-Simons invariants of
cyclic coverings of the hyperbolic knot orbifolds. For the
fundamental group of knot, 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.Comment: 9 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1601.00723, arXiv:1607.0804
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