We survey Ozsvath-Szabo's bordered approach to knot Floer homology. After a quick introduction to knot Floer homology, we introduce the relevant algebraic concepts (A8-modules, type D-structures, box tensor product, etc.), we discuss partial Kauffman states, the construction of the boundary algebra, and sketch Ozsvath and Szabo'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 Ozsvath and Szabo (`Kauffman states, bordered algebras, and a bigraded knot invariant', 2016. arXiv:1603.06559) are replaced here by an associative algebra C(n). These are the notes of two lecture series delivered by Peter Ozsvath and Zoltan Szabo at Princeton University during the summer of 2018.
展开▼
