A bordered HF- algebra for the torus

Robert Lipshitz; Peter Ozsváth; Dylan Thurston

doi:10.4310/jsg.250403021401

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arXiv · 2108.12488

A bordered HF- algebra for the torus

Robert Lipshitz·Peter Ozsváth·Dylan Thurston

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Abstract

We describe a weighted $A_\infty$-algebra associated to the torus. We give a combinatorial construction of this algebra, and an abstract characterization. The abstract characterization also gives a relationship between our algebra and the wrapped Fukaya category of the torus. These algebras underpin the (unspecialized) bordered Heegaard Floer homology for three-manifolds with torus boundary, which will be constructed in forthcoming work.

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Robert Lipshitz, Peter Ozsváth, Dylan Thurston. 2021-08-27. A bordered HF- algebra for the torus. https://doi.org/10.4310/jsg.250403021401

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