The hyperbolic volume of knots from quantum dilogarithm

Abstract

The invariant of a link in three-sphere, associated with the cyclic quantum dilogarithm, depends on a natural number $N$. By the analysis of particular examples it is argued that for a hyperbolic knot (link) the absolute value of this invariant grows exponentially at large $N$, the hyperbolic volume of the knot (link) complement being the growth rate.

8 pages, LaTeX, no figures, minor changes with additional references, to appear in Lett. Math. Phys

References in corpus (3)

• Discrete Heisenberg-Weyl Group and Modular Group
• Quantum Dilogarithm
• A Link Invariant from Quantum Dilogarithm

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