Classification of links with Khovanov homology of minimal rank

2019/09/22 by Yi Xie, Xie, Yi, Boyu Zhang +1
Computer Science · Mathematics · #57M27 #57R58 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1909.10032

openalex publication_date 2019/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If L is an oriented link with n components, then the rank of its Khovanov homology is at least 2ⁿ. 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.

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