Mathematical Research Letters

Volume 26 (2019)

Number 5

Khovanov homology detects the Hopf links

Pages: 1281 – 1290



John A. Baldwin (Department of Mathematics, Boston College, Chestnut Hill, Massachusetts, U.S.A.)

Steven Sivek (Department of Mathematics, Imperial College London, United Kingdom)

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


We prove that any link in $S^3$ whose Khovanov homology is the same as that of a Hopf link must be isotopic to that Hopf link. This holds for both reduced and unreduced Khovanov homology, and with coefficients in either $\mathbb{Z}$ or $\mathbb{Z} / 2 \mathbb{Z}$.

J.A.B. was supported by NSF CAREER Grant DMS-1454865.

Received 19 March 2019

Accepted 4 June 2019

Published 27 November 2019