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

Ji Young Ham, Joongul Lee, Alexander Mednykh, Aleksei Rasskazov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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(2n, 4).

Original languageEnglish
Article number1750082
Number of pages22
JournalJournal of Knot Theory and its Ramifications
Volume26
Issue number12
DOIs
Publication statusPublished - 1 Oct 2017

Keywords

  • 2-bridge knot
  • Chern-Simons invariant
  • cone-manifold
  • explicit formula
  • Fundamental set
  • knot with Conway's notation C (2n, 4)
  • orbifold
  • Riley-Mednykh polynomial
  • volume
  • TWIST KNOTS
  • REPRESENTATION
  • knot with Conway's notation C(2n, 4)
  • FORMULA
  • COMPLEX VOLUMES
  • HYPERBOLIC 3-MANIFOLDS
  • RIGIDITY
  • CONE-MANIFOLDS
  • ETA-INVARIANT

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