Hyperbolic structure arising from a knot invariant

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Abstract

We study the knot invariant based on the quantum dilogarithm function. This invariant can be regarded as a noncompact analog of Kashaev's invariant, or the colored Jones invariant, and is defined by an integral form. The three-dimensional picture of our invariant originates from the pentagon identity of the quantum dilogarithm function, and we show that the hyperbolicity consistency conditions in gluing polyhedra arise naturally in the classical limit as the saddle point equation of our invariant.

Original languageEnglish
Pages (from-to)3309-3333
Number of pages25
JournalInternational Journal of Modern Physics A
Volume16
Issue number19
DOIs
Publication statusPublished - Jul 30 2001

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All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics

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