A universal U(1)-RCC invariant of links and rationality conjecture

Abstract

We define a graph algebra version of the stationary phase integration over the coadjoint orbits in the Reshetikhin formula for the colored Jones-HOMFLY polynomial. As a result, we obtain a `universal' U(1)-RCC invariant of links in rational homology spheres, which determines the U(1)-RCC invariants based on simple Lie algebras. We formulate a rationality conjecture about the structure of this invariant.

arXiv comment107 pages

References in corpus (3)

• The lines of the Kontsevich integral and Rozansky's rationality conjecture
• A contribution of a U(1)-reducible connection to quantum invariants of links I: R-matrix and Burau representation
• A contribution of a U(1)-reducible connection to quantum invariants of links II: Links in rational homology spheres

Cited by in corpus (4)

• Asymptotics of the colored Jones function of a knot
• The Jacobian Conjecture as a Problem of Perturbative Quantum Field Theory
• On the LMO conjecture
• Knot invariants derived from the equivariant linking pairing