Results 1 
5 of
5
Threedimensional quantum gravity, ChernSimons theory, and the Apolynomial
, 2003
"... We study threedimensional ChernSimons theory with complex gauge group SL(2,C), which has many interesting connections with threedimensional quantum gravity and geometry of hyperbolic 3manifolds. We show that, in the presence of a single knotted Wilson loop in an infinitedimensional representati ..."
Abstract

Cited by 78 (11 self)
 Add to MetaCart
(Show Context)
We study threedimensional ChernSimons theory with complex gauge group SL(2,C), which has many interesting connections with threedimensional quantum gravity and geometry of hyperbolic 3manifolds. We show that, in the presence of a single knotted Wilson loop in an infinitedimensional representation of the gauge group, the classical and quantum properties of such theory are described by an algebraic curve called the Apolynomial of a knot. Using this approach, we find some new and rather surprising relations between the Apolynomial, the colored Jones polynomial, and other invariants of hyperbolic 3manifolds. These relations generalize the volume conjecture and the MelvinMortonRozansky conjecture, and suggest an intriguing connection between the SL(2,C) partition function and the colored Jones polynomial.
Construction and recognition of hyperbolic 3manifolds with geodesic boundary
"... ..."
(Show Context)
unknown title
"... Invariants of links with flat connections in their complements.II. Holonomy Rmatrices related to quantized universal enveloping algebras at roots of 1. R. Kashaev, N.Reshetikhin ..."
Abstract
 Add to MetaCart
(Show Context)
Invariants of links with flat connections in their complements.II. Holonomy Rmatrices related to quantized universal enveloping algebras at roots of 1. R. Kashaev, N.Reshetikhin