The colored Jones polynomial and the A-polynomial of Knots☆
By Thang T. Q. Lê. 2004
112 citations recorded by the source corpus.
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. The AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial is established for a large class of two-bridge knots, including all twist knots. We formulate a weaker conjecture and prove that it holds for all two-bridge knots. Along the way we also calculate the Kauffman bracket skein module of the complements of two-bridge knots. Some properties of the colored Jones polynomial are established.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a649746bda4d24b956e7a8c00954bd8ba9ad805b
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The Jones slopes of a knot (2009, background): “K and σK. This was shown by Kauffman, Murasugi and Thistlethwaite, [Kf, Mu, Th], and further simplified by Turaev [Tu1]. See also [Li, p.42] and [Le, Prop.2.1]. With our conventions, Proposition 2.1 of [Le] states that for all n we have: δK(n) = (cK +wK) 4 n2 + −|A| +2c+ K +1 2 (16) n δ∗ K(n) = (−cK +”
- Confluence Theory for Graphs (2006, unknown): “(For more on Kauffman bracket skein modules see Bullock [7; 8], Bullock–Frohman–Kania-Bartoszyńska [9; 10], Blanchet–Habegger–Masbaum– Vogel [5], Bullock–Przytycki [11], Frohman–Gelca [15], Frohman–Gelca–Lofaro [16], Frohman–Kania-Bartoszyńska [17], Gelca–Sain [20; 19], Gilmer–Harris [21], Hoste– Pr”
- Asymptotics of the colored Jones function of a knot (2005, unknown): “In [22] the second author showed that there are quadratic bounds for the degrees of the colored Jones polynomial.”