Koszul duality and the link surgery formula

Ian Zemke

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arXiv · 2507.09964

Koszul duality and the link surgery formula

Ian Zemke

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Abstract

In previous works, the author described an associative algebra whose $A_\infty$-module categories encode the Heegaard Floer Dehn surgery formulas. In this article, we describe the Koszul dual of this algebra. We construct dualizing bimodules, and prove several equivalences of categories. The constructions of this paper have applications to computational problems involving the link surgery formula.

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Ian Zemke. 2025-07-14. Koszul duality and the link surgery formula. https://arxiv.org/abs/2507.09964

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