On the volume and the Chern-Simons invariant for the $2$-bridge knot orbifolds

Abstract

We extend some part of the unpublished paper written by Mednykh and Rasskazov. Using the approach indicated in this paper we derive the Riley-Mednykh polynomial for some family of the $2$-bridge knot orbifolds. As a result we obtain explicit formulae for the volume of cone-manifolds and the Chern-Simons invariant of orbifolds of the knot with Conway's notation $C(2n,4)$.

20 pages, 8 figures, 5 tables. arXiv admin note: text overlap with arXiv:1601.00723, arXiv:1512.05481

References in corpus (2)

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

Cited by in corpus (2)

• Explicit formulae for Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation $C(2n,3)$
• The A-polynomial 2-tuple of twisted Whitehead links