Khovanov homology detects the Hopf links

TL;DR

This paper proves that Khovanov homology uniquely identifies Hopf links in S^3, establishing it as a complete invariant for these links across various coefficients and versions.

Contribution

It demonstrates that Khovanov homology detects Hopf links, a significant step in understanding the power of this invariant.

Findings

Khovanov homology distinguishes Hopf links from all other links.

The result holds for both reduced and unreduced homology.

It applies over integer and mod 2 coefficients.

Abstract

We prove that any link in $S^3$ whose Khovanov homology is the same as that of a Hopf link must be isotopic to that Hopf link. This holds for both reduced and unreduced Khovanov homology, and with coefficients in either $\mathbb{Z}$ or $\mathbb{Z}/2\mathbb{Z}$.