Classification of links with Khovanov homology of minimal rank

Yi Xie; Boyu Zhang

doi:10.4171/jems/1380

JournalsjemsVol. 27, No. 1pp. 333–394

Classification of links with Khovanov homology of minimal rank

Yi Xie
Peking University, Beijing, P. R. China
- MathSciNet
- ORCID
Boyu Zhang
University of Maryland at College Park, College Park, USA
- MathSciNet
- ORCID

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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).

Cite this article

Yi Xie, Boyu Zhang, Classification of links with Khovanov homology of minimal rank. J. Eur. Math. Soc. 27 (2025), no. 1, pp. 333–394

DOI 10.4171/JEMS/1380