Overview of knot invariants at roots of unity

Abstract

We discuss different invariants of knots and links that depend on a primitive root of unity. We clarify the definitions of existing invariants with the Reshetikhin-Turaev method, present the generalization of ADO invariants to ${\mathcal{U}}_q(s{l}_N)$ and highlight the connections between different invariants.

arXiv comment8 pages, 6 figures

References in corpus (6)

• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• Chern-Simons Theory in the Temporal Gauge and Knot Invariants through the Universal Quantum R-Matrix
• Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid
• Distinguishing Mutant Knots
• Representations of U_q(sl(N)) at Roots of Unity
• Difference of mutant knot invariants and their differential expansion

Cited by in corpus (2)

• Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
• Invariants of knots and links at roots of unity