Letters in Mathematical Physics

, Volume 39, Issue 3, pp 269–275

The Hyperbolic Volume of Knots from the Quantum Dilogarithm


DOI: 10.1023/A:1007364912784

Cite this article as:
KASHAEV, R.M. Letters in Mathematical Physics (1997) 39: 269. doi:10.1023/A:1007364912784


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 theoryhyperbolic 3-manifoldstopological quantum field theory.

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

    • 1
  1. 1.Laboratoire de Physique Thé ENSLAPP**ENSLyonLyonFrance