Khovanov–Seidel quiver algebras and Ozsváth–Szabó's bordered theory

2016/05/25 by Andrew Manion · 11 citations
Mathematics · Medicine · #Algebra over a field #Bimodule #Botulinum Toxin and Related Neurological Disorders #Categorification #Cohomology #Floer homology #Functor #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Khovanov homology #Knot (papermaking) #Mathematics #Orbifold #Pure mathematics #Quiver #Quotient #Symplectic geometry #math.GT #msc:57M27

paper · pdf · doi:10.1016/j.jalgebra.2017.05.029

published in Journal of Algebra 488, 110-144 (Elsevier BV) · 28 pages; 15 figures

arxiv created 2016/05/25 · openalex publication_date 2017/06/15 · arxiv updated 2017/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We investigate a relationship between Ozsváth and Szabó's bordered theory and the algebras and bimodules constructed by Khovanov-Seidel. Specifically, we show that (a variant of) a special case of Ozsváth-Szabó's algebras has a quotient which is isomorphic to the Khovanov-Seidel quiver algebra with coefficients in ℤ/2ℤ. Furthermore, we show that after induction and restriction of scalars, the dg bimodule over quiver algebras associated to a crossing by Khovanov-Seidel is homotopy equivalent to Ozsváth-Szabó's DA bimodule for the crossing in this special case.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants
• On the Heegaard Floer homology of branched double-covers
• Heegaard Floer homology and alternating knots
• Matrix factorizations and link homology II
• A categorification of the Jones polynomial
• A Categorification of the HOMFLY-PT Polynomial with a Spectral Sequence to Knot Floer Homology

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