Singular crossings and Ozsváth–Szabó’s Kauffman-states functor
Volume 253 / 2021
Fundamenta Mathematicae 253 (2021), 61-120
MSC: Primary 57K18; Secondary 57R58, 57R56.
DOI: 10.4064/fm762-5-2020
Published online: 21 September 2020
Abstract
Recently, Ozsváth and Szabó introduced some algebraic constructions computing knot Floer homology in the spirit of bordered Floer homology, including a family of algebras $\mathcal B (n)$ and, for a generator of the braid group on $n$ strands, a certain type of bimodule over $\mathcal B (n)$. We define analogous bimodules for singular crossings. Our bimodules are motivated by counting holomorphic disks in a bordered sutured version of a Heegaard diagram considered previously by Ozsváth, Stipsicz, and Szabó.
