An Ozsváth--Szabó-type spectral sequence for links in S¹× S²

2024/03/14 by Jesse Cohen, Cohen, Jesse
Mathematics · Physics and Astronomy · #57K18 (primary) 57R58 #57M12 (secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2403.09790

openalex publication_date 2024/03/14 · openalex created_date 2024/03/19 · openalex updated_date 2026/07/28

Abstract

We show that there is a spectral sequence with E²-page given by the Khovanov homology of a link in S¹× S², as defined by Rozansky in arXiv:1011.1958, which converges to the Hochschild homology of an A_∞-bimodule defined in terms of bordered Floer invariants. We also show that the homology algebras H_*\mathfrakh_n of the algebras \mathfrakh_n over which these bimodules are defined give nontrivial A_∞-deformations of Khovanov's arc algebras H_n for n>1.

Related

• The Ozsváth-Szabó spectral sequence and combinatorial link homology
• A spectral sequence in odd Khovanov homology (Eine Spektralsequenz in ungerader Khovanov-Homologie)
• On the spectral sequence from Khovanov homology to Heegaard Floer homology
• A perturbation of the geometric spectral sequence in Khovanov homology
• An integral lift, starting in odd Khovanov homology, of Szabó's spectral sequence