TL;DR
This paper explores the Koszul dual of an algebra related to Heegaard Floer Dehn surgery formulas, providing new categorical equivalences and dualizing bimodules with applications to computational link surgery problems.
Contribution
It introduces the Koszul dual of a key algebra in Heegaard Floer theory, along with dualizing bimodules and categorical equivalences, advancing the algebraic understanding of link surgery formulas.
Findings
Construction of the Koszul dual algebra
Development of dualizing bimodules
Establishment of categorical equivalences
Abstract
In previous works, the author described an associative algebra whose -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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