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

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 $\mathbb{Z}/2\mathbb{Z}$. 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.

28 pages; 15 figures

References in corpus (2)

• Floer homology and knot complements
• A Categorification of the HOMFLY-PT Polynomial with a Spectral Sequence to Knot Floer Homology

Cited by in corpus (6)

• Algebras with matchings and knot Floer homology
• Ozsvath-Szabo bordered algebras and subquotients of category O
• Strands algebras and Ozsváth-Szabó's Kauffman-states functor
• DG structures on odd categorified quantum sl(2)
• From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron
• Trivalent vertices and bordered knot Floer homology in the standard basis