Khovanov invariants via Fukaya categories: the tangle invariants agree

2020/04/03 by Artem Kotelskiy, Liam Watson, Kotelskiy, Artem +3
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2004.01619

openalex publication_date 2020/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a pointed 4-ended tangle T ⊂ D³, there are two Khovanov theoretic tangle invariants, \unicode1044₁(T) from [arXiv:1910.1458] and L_T from [arXiv:1808.06957], which are twisted complexes over the Fukaya category of the boundary 4-punctured sphere (S²,4pt)=∂ (D³, T). We prove that these two invariants are the same.

Citations

• Bordered Heegaard Floer homology
• Immersed curves in Khovanov homology

Related

• 2-cabling and tangle operators in Khovanov theory
• Khovanov homology and the Fukaya category of the traceless character variety for the twice-punctured torus
• Immersed curves in Khovanov homology
• A computation in Khovanov-Rozansky Homology
• Khovanov homology for alternating tangles