Kashaev's conjecture and the chern-simons invariants of knots and links

Hitoshi Murakami, Jun Murakami, Miyuki Okamoto, Toshie Takata, Yoshiyuki Yokota

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

R. M. Kashaev conjectured that the asymptotic behavior of the link invariant he introduced [Kashaev 95], which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volume of any hyperbolic link complement. We observe numerically that for knots 63, 89 and 820 and for the Whitehead link, the colored Jones polynomials are related to the hyperbolic volumes and the Chern-Simons invariants and propose a complexification of Kashaev's conjecture.

Original languageEnglish
Pages (from-to)427-435
Number of pages9
JournalExperimental Mathematics
Volume11
Issue number3
DOIs
Publication statusPublished - 2002 Jan 1

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Keywords

  • Chern-simons invariant
  • Colored jones polynomial
  • Kashaev’s conjecture
  • Volume
  • Volume conjecture

ASJC Scopus subject areas

  • Mathematics(all)

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