Mathematical Research Letters

Volume 29 (2022)

Number 4

On links with Khovanov homology of small ranks

Pages: 1261 – 1277

DOI: https://dx.doi.org/10.4310/MRL.2022.v29.n4.a14

Authors

Yi Xie (Beijing International Center for Mathematical Research, Peking University, Beijing, China)

Boyu Zhang (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)

Abstract

We classify all links whose Khovanov homology have ranks no greater than $8$, and all three-component links whose Khovanov homology have ranks no greater than $12$, where the coefficient ring is $\mathbb{Z}/2$. The classification is based on the previous results of Kronheimer–Mrowka [8], Batson–Seed [3], Baldwin–Sivek [1], and the authors [19].

Full Text (PDF format)

The first author is supported by National Key R&D Program of China SQ2020YFA0712800 and NSFC 12071005.

Received 23 July 2020

Accepted 5 September 2020

Published 23 February 2023