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

Da Vinci College of General Education, Chung-Ang University, General Education Building, 84 HeukSeok-Ro, DongJak-Gu, Seoul 06974, Korea

E-mail Address: jyham@cau.ac.kr

Corresponding author.

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Joongul Lee

Department of Mathematics Education, Hongik University, 94 Wausan-ro, Mapo-gu, Seoul 04066, Korea

E-mail Address: jglee@hongik.ac.kr

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Alexander Mednykh

Sobolev Institute of Mathematics, pr. Kotyuga 4, Novosibirsk 630090, Russia

Novosibirsk State University, Pirogova 2, Novosibirsk 630090, Russia

E-mail Address: mednykh@math.nsc.ru

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, and

Aleksei Rasskazov

School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, AUT Tower, 2-14 Wakefield Street, Auckland 1010, New Zealand

E-mail Address: aleksei.rasskazov@aut.ac.nz

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https://doi.org/10.1142/S0218216517500821Cited by:6 (Source: Crossref)

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 $2$ -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 $C (2 n, 4)$ .

Keywords:

AMSC: 57M25, 57M27

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