On Kontsevich integral of torus knots
arXiv:math/0310111
Abstract
We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.
10 pages, 4 figures
References in corpus (8)
- Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
- The lines of the Kontsevich integral and Rozansky's rationality conjecture
- Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial
- Wheeling: A diagrammatic analogue of the Duflo isomorphism
- Non injectivity of the "hair" map
- Whitehead doubling persists
- Finite type invariants of cyclic branched covers
- A cabling formula for the 2-loop polynomial of knots