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 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.

52 pages, 24 figures; added Corollary 1.3, Corollary 1.4, and Theorem 1.6 in version 2; simplified the proof of Lemma 9.2 (previously Lemma 9.7) in version 3