Hyperbolic structure arising from a knot invariant

Kazuhiro Hikami

doi:10.1142/S0217751X0100444X

Hyperbolic structure arising from a knot invariant

Kazuhiro Hikami

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

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 language	English
Pages (from-to)	3309-3333
Number of pages	25
Journal	International Journal of Modern Physics A
Volume	16
Issue number	19
DOIs	https://doi.org/10.1142/S0217751X0100444X
Publication status	Published - Jul 30 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

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10.1142/S0217751X0100444X

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Hyperbolic structure arising from a knot invariant

Abstract

All Science Journal Classification (ASJC) codes

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