Classification of links with Khovanov homology of minimal rank

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 links that achieve 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 (2015).