Knot-quiver correspondence: a brief review

TL;DR

This paper reviews the knot-quiver correspondence, connecting symmetric quivers and their partition functions to quantum invariants of knots and links in three-dimensional space.

Contribution

It provides a concise overview of how symmetric quivers relate to quantum knot invariants through motivic Donaldson-Thomas series.

Findings

Clarifies the relationship between quiver partition functions and knot invariants

Summarizes key aspects of the knot-quiver correspondence

Highlights the role of motivic Donaldson-Thomas series in knot theory

Abstract

This note is an overview of the knot-quiver correspondence, which relates symmetric quivers and their partition functions, a.k.a. motivic Donaldson-Thomas generating series, to quantum invariants of knots and links in $S^3$.