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

Abstract

This paper extends the work by Mednykh and Rasskazov presented in [On the structure of the canonical fundamental set for the 2-bridge link orbifolds, Universität Bielefeld, Sonderforschungsbereich 343, Discrete Structuren in der Mathematik, Preprint (1988), pp. 98–062, www.mathematik.uni-bielefeld.de/sfb343/preprints/pr98062.ps.gz ]. By using their approach, we derive the Riley–Mednykh polynomial for a family of [Formula: see text]-bridge knot orbifolds. As a result, we obtain explicit formulae for the volumes and Chern–Simons invariants of orbifolds and cone-manifolds on the knot with Conway’s notation [Formula: see text].