Explicit formulae for Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation $C(2n,3)$

Abstract

We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation $C(2n,3)$ using the Schläfli formula for the generalized Chern-Simons function on the family of $C(2n,3)$ 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 $C(2n,3)$ orbifolds.

arXiv comment10 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1411.2383

References in corpus (6)

• Extended Bloch group and the Cheeger-Chern-Simons class
• Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds
• The volume and Chern-Simons invariant of a representation
• Deforming Euclidean cone 3-manifolds
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Cited by in corpus (5)

• On the volume and the Chern-Simons invariant for the $2$-bridge knot orbifolds
• Cohomological invariants of representations of 3-manifold groups
• An explicit formula for the $A$-polynomial of the knot with Conway's notation $C(2n,3)$
• On the volume and the Chern-Simons invariant for the hyperbolic alternating knot orbifolds
• Explicit formulae for Chern-Simons invariants of the hyperbolic $J(2n,-2m)$ knot orbifolds