Classification of links with Khovanov homology of minimal rank

TL;DR

This paper classifies all links whose Khovanov homology over Z/2 coefficients attains the minimal possible rank, showing they are constructed from Hopf links and unknots via connected sums and disjoint unions.

Contribution

It provides a complete classification of links with minimal Khovanov homology rank, answering a question posed by Batson and Seed.

Findings

Links with minimal Khovanov homology rank are built from Hopf links and unknots.

Such links are obtained through iterated connected sums and disjoint unions.

The classification confirms the lower bound of 2^n for n-component links.

Abstract

If L is an oriented link with $n$ components, then the rank of its Khovanov homology is at least $2^n$. We classify all the links whose Khovanov homology with Z/2-coefficients achieves this lower bound, and show that such links can be obtained by iterated connected sums and disjoint unions of Hopf links and unknots. This gives a positive answer to a question asked by Batson and Seed.