Jones polynomials in fundamental and adjoint representations

We provide the data for Jones polynomials of all hyperbolic knots up to 16 crossings in the file data-name-vol-J2.h5, and data for 3-dimensional colored Jones polynomials of a significant fraction of hyperbolic knots up to 15 crossings in the file data-name-vol-J2-J3.h5.

The file data-name-vol-J2-J3.h5 contains the names of knots, volumes of knots, 2-dimensional Jones polynomials and 3-dimensional Jones polynomials for 177,296 hyperbolic knots up to 15 crossings. The names, volumes, and 2-d Jones polynomials can be calculated using the KnotTheory package from KnotAtlas. Our main contribution is the calculation of the 3-dimensional Jones polynomials using vertex model techniques. This data is used in the paper "Colored Jones Polynomias and the Volume Conjecture" for Machine Learning experiments and other numerical analysis.

The file data-name-vol-J2.h5 contains the names of knots, volumes of knots, 2-dimensional Jones polynomials of the 1,701,903 hyperbolic knots up to 16 crossings, all calculated using the KnotTheory package from KnotAtlas.

In both files, the top level datasets are called "names", "volumes", "jones2", and if present, "jones3".