Khovanov homology detects the figure-eight knot

TL;DR

This paper proves that reduced Khovanov homology over the rationals uniquely identifies the figure-eight knot, establishing a significant link between Khovanov homology and knot detection.

Contribution

It demonstrates that reduced Khovanov homology detects the figure-eight knot using Dowlin's spectral sequence, a novel application in knot theory.

Findings

Reduced Khovanov homology over $\\mathbb{Q}$ detects the figure-eight knot.

Establishes a new connection between Khovanov homology and knot detection.

Utilizes Dowlin's spectral sequence to prove knot detection results.

Abstract

Using Dowlin's spectral sequence from Khovanov homology to knot Floer homology, we prove that reduced Khovanov homology (over $\mathbb{Q}$) detects the figure-eight knot.