HYPERBOLIC STRUCTURE ARISING FROM A KNOT INVARIANT
- 30 July 2001
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics A
- Vol. 16 (19), 3309-3333
- https://doi.org/10.1142/s0217751x0100444x
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.Keywords
This publication has 19 references indexed in Scilit:
- Bloch invariants of hyperbolic 3-manifoldsDuke Mathematical Journal, 1999
- A LINK INVARIANT FROM QUANTUM DILOGARITHMModern Physics Letters A, 1995
- QUANTUM DILOGARITHMModern Physics Letters A, 1994
- Topological gauge theories and group cohomologyCommunications in Mathematical Physics, 1990
- Quantum field theory and the Jones polynomialCommunications in Mathematical Physics, 1989
- The Yang-Baxter equation and invariants of linksInventiones Mathematicae, 1988
- The ?-invariant of hyperbolic 3-manifoldsInventiones Mathematicae, 1985
- Volumes of hyperbolic three-manifoldsTopology, 1985
- A polynomial invariant for knots via von Neumann algebrasBulletin of the American Mathematical Society, 1985
- Hyperbolic geometry: The first 150 yearsBulletin of the American Mathematical Society, 1982