nLab colored Jones polynomial

Idea

The colored Jones polynomial of a knot or link is a generalization of the Jones polynomial. The latter may be seen as ‘colored’ by the defining 2-dimensional complex linear representation of SU(2), where the $N$-colored Jones polynomial $J_N(K, q)$ involves instead the $N$-dimensional irreducible representation.

Related concepts

• volume conjecture

References

• Stavros Garoufalidis, Martin Loebl, A non-commutative formula for the colored Jones function (arXiv:math/0411505)

Relation of the colored Jones polynomial to Lie algebra weight systems on chord diagrams:

• Dror Bar-Natan, Stavros Garoufalidis, On the Melvin–Morton–Rozansky conjecture, Invent math (1996) 125: 103 (doi:10.1007/s002220050070, pdf)

In relation to the volume conjecture:

• Hitoshi Murakami and Jun Murakami, The Colored Jones Polynomial And The Simplicial Volume Of A Knot, Acta Math. 186 (2001) 85-104 (euclid.acta/1485891370)