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arXiv · 1605.08082

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

Andrew Manion
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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.

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Andrew Manion. 2016-05-25. Khovanov-Seidel quiver algebras and Ozsváth-Szabó's bordered theory. https://doi.org/10.1016/j.jalgebra.2017.05.029

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