Singular crossings and Ozsváth-Szabó’s Kauffman-states functor. (English) Zbl 1526.57012
Motivated by the construction of bordered knot Floer homology due to Ozsváth and Szabó, the author defines bimodules associated to singular crossings of knot projections. Bordered knot Floer homology allows for efficient computations of knot Floer homology by means of bimodules associated to crossings (or, more generally, tangles). The paper under review gives a conjectural counterpart of these bimodules for singular crossings of projections, by defining bimodules that satisfy all the necessary algebraic requirement, and that are inspired by a pseudo-holomorphic count in a suitable multiply-pointed bordered Heegaard diagram.
Reviewer: Marco Golla (Nantes)
MSC:
| 57K18 | Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) |
| 57R58 | Floer homology |
| 57R56 | Topological quantum field theories (aspects of differential topology) |
Software:
HFKcalcReferences:
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