The Colored Jones Polynomial of Singular Knots

Abstract

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 Kauffman-Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group representations.

Cited by in corpus (3)

• A $q$-series identity via the ${\mathfrak{sl}}_3$ colored Jones polynomials for the $(2,2m)$-torus link
• Foundations of the Colored Jones Polynomial of singular knots
• $A_2$ colored polynomials of rigid vertex graphs