The Hyperbolic Volume of Knots from the 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 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.
- Publication:
-
Letters in Mathematical Physics
- Pub Date:
- February 1997
- DOI:
- 10.1023/A:1007364912784
- arXiv:
- arXiv:q-alg/9601025
- Bibcode:
- 1997LMaPh..39..269K
- Keywords:
-
- knot theory;
- hyperbolic 3-manifolds;
- topological quantum field theory.;
- Mathematics - Quantum Algebra
- E-Print:
- 8 pages, LaTeX, no figures, minor changes with additional references, to appear in Lett. Math. Phys