2018/11/18 by Alfieri, Antonio, Van Dyke, Jackson
#FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1811.07348
We survey Ozsváth-Szabó's bordered approach to knot Floer homology. After a quick introduction to knot Floer homology, we introduce the relevant algebraic concepts (A_∞-modules, type D-structures, box tensor, etc.), we discuss partial Kauffman states, the construction of the boundary algebra, and sketch Ozsváth and Szabó's analytic construction of the type D-structure associated to an upper diagram. Finally we give an explicit description of the structure maps of the DA-bimodules of some elementary partial diagrams. These can be used to perform explicit computations of the knot Floer differential of any knot in S3. The boundary DGAs B(n,k) and A(n,k) of [7] are replaced here by an associative algebra C(n). These are the notes of two lecture series delivered by Peter Ozsváth and Zoltán Szabó at Princeton University during the summer of 2018.