A bordered HF- algebra for the torus
Robert Lipshitz, Peter Ozsváth, Dylan Thurston
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.