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In this paper, we examine the properties of the Jones polynomial using dimensionality
reduction learning techniques combined with ideas from topological data analysis. Our data …

We generalize the colored Jones polynomial to $4 $-valent graphs. This generalization is
given as a sequence of invariants in which the first term is a one variable specialization of …

The colored Jones polynomial is a $ q $-polynomial invariant of links colored by irreducible
representations of a simple Lie algebra. A $ q $-series called a tail is obtained as the limit of …

The colored 𝔰 𝔩 3 Jones polynomials J (n 1, n 2) 𝔰 𝔩 3 (L; q) are given by a link and an (n 1,
n 2)-irreducible representation of 𝔰 𝔩 3. In general, it is hard to calculate J (n 1, n 2) 𝔰 𝔩 3 …

The sl 3 sl_3 colored Jones polynomial J λ sl 3 (L) J_λ^sl_3(L) is obtained by coloring the
link components with two-row Young diagram λ. Although it is difficult to compute J λ sl 3 (L) …

This thesis concerns modularity properties of Nahm sums, a family of q-hypergeometric
series, and applications. They appear, for example, as characters of VOAs, knot invariants …

The colored Jones polynomial is a knot invariant that plays a central role in low dimensional
topology. We give a simple and an efficient algorithm to compute the colored Jones …

This article gives the foundations of the colored Jones polynomial for singular knots. We
extend Masbum and Vogel's algorithm to compute the colored Jones polynomial for any …

We prove that the coefficients of the colored Jones polynomial of alternating links stabilize
under increasing the number of twists in the twist regions of the link diagram. This gives us …