22,525 research outputs found
The Colored Jones Polynomial and the A-Polynomial of Knots
We study relationships between the colored Jones polynomial and the
A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ
conjecture (of Garoufalidis) that relates the colored Jones polynomial and the
A-polynomial. Along the way we also calculate the Kauffman bracket skein module
of all 2-bridge knots. Some properties of the colored Jones polynomial of
alternating knots are established.Comment: Typos and minor mistakes corrected. To appear in Advances in
Mathematic
On Denominators of the Kontsevich Integral and the Universal Perturbative Invariant of 3-Manifolds
The integrality of the Kontsevich integral and perturbative invariants is
discussed. We show that the denominator of the degree part of the
Kontsevich integral of any knot or link is a divisor of .
We also show that the denominator of of the degree part of the universal
perturbative invariant of homology 3-spheres is not divisible by any prime
greater than .Comment: 27 pages, LaTeX with graphics packag
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