Overview of knot invariants at roots of unity

TL;DR

This paper reviews various knot and link invariants at roots of unity, clarifies their definitions via Reshetikhin-Turaev, and explores generalizations and connections among these invariants.

Contribution

It provides a comprehensive overview of invariants at roots of unity, including generalizations of ADO invariants to quantum groups beyond sl_2.

Findings

Clarification of existing invariants' definitions

Generalization of ADO invariants to U_q(sl_N)

Connections established between different invariants

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 $\mathcal{U}_q(sl_N)$ and highlight the connections between different invariants.