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Annular Khovanov homology and augmented links

Hongjian Yang

Algebraic & Geometric Topology 24 (2024) 325–339
Abstract

Given an annular link L, there is a corresponding augmented link L~ in S3 obtained by adding a meridian unknot component to L. We construct a spectral sequence with the second page isomorphic to the annular Khovanov homology of L that converges to the reduced Khovanov homology of L~. As an application, we classify all the links with the minimal rank of annular Khovanov homology. We also give a proof that annular Khovanov homology detects unlinks.

Keywords
Khovanov homology
Mathematical Subject Classification
Primary: 57K18
References
Publication
Received: 6 September 2021
Revised: 18 August 2022
Accepted: 18 October 2022
Published: 18 March 2024
Authors
Hongjian Yang
Department of Mathematics
Stanford University
Stanford, CA
United States

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