Article

Letters in Mathematical Physics

, Volume 39, Issue 3, pp 269-275

First online:

The Hyperbolic Volume of Knots from the Quantum Dilogarithm

  • R. M. KASHAEVAffiliated withLaboratoire de Physique Thé ENSLAPP**, ENSLyon

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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 particularexamples, it is argued that, for a hyperbolic knot (link), the absolute valueof this invariant grows exponentially at large N, the hyperbolic volume of the knot (link) complement being the growth rate.

knot theory hyperbolic 3-manifolds topological quantum field theory.