2024/08/02 by Khan, Isabella
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2408.01564
By slicing the Heegaard diagram for a given 3-manifold in a particular way, it is possible to construct A∞-bimodules, the tensor product of which retrieves the Heegaard Floer homology of the original 3-manifold. The first step in this is to construct algebras corresponding to the individual slices. Here, we use the graphical calculus for A∞-structures introduced by Lipshitz, Ozsváth, and Thurston, to construct Koszul dual weighted A∞-algebras A and B, and dualizing bimodules for a particular star-shaped class of slice. The duality result is then proved in the sequel.