Geometry and Topology Seminar

Ozsváth and Szabó introduced in 2016 a knot invariant, which they announced to be isomorphic to the usual knot Floer homology. Their construction is reminiscent of bordered Floer homology: for example, their invariant is defined by tensoring bimodules over certain algebras.

During the talk I will introduce a more geometric construction, closer in spirit to bordered sutured Floer homology, based on strands on a particular class of generalised arc diagrams. The resulting strands algebras are quasi-isomorphic to the Ozsváth-Szabó algebras, suggesting that Ozsváth and Szabó's theory may be part of a hypothetical generalisation of bordered sutured Floer homology. This is a joint work with Mike Willis and Andy Manion.