Geodesic
A mnemonic for the Lipshitz–Ozsváth–Thurston correspondence
Kotelskiy, Artem1 ; Watson, Liam2 ; Zibrowius, Claudius3
1 Department of Mathematics, Indiana University, Bloomington, IN, United States, Department of Mathematics, Stony Brook University, Stony Brook, NY, United States
2 Department of Mathematics, University of British Columbia, Vancouver, BC, Canada
3 Faculty of Mathematics, University of Regensburg, Regensburg, Germany, Department of Mathematical Sciences, Durham University, Durham, United Kingdom
Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2519-2543

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

When k is a field, type D structures over the algebra k[u,v]∕(uv) are equivalent to immersed curves decorated with local systems in the twice-punctured disk. Consequently, knot Floer homology, as a type D structure over k[u,v]∕(uv), can be viewed as a set of immersed curves. With this observation as a starting point, given a knot K in S3, we realize the immersed curve invariant HF^(S3 \ ν ∘(K)) of Hanselman, Rasmussen and Watson by converting the twice-punctured disk to a once-punctured torus via a handle attachment. This recovers a result of Lipshitz, Ozsváth and Thurston calculating the bordered invariant of S3 \ ν ∘(K) in terms of the knot Floer homology of K.

DOI : 10.2140/agt.2023.23.2519
Keywords: Fukaya categories of punctured surfaces, bordered Heegaard Floer theory, multicurve invariants, knot Floer homology

Kotelskiy, Artem 1 ; Watson, Liam 2 ; Zibrowius, Claudius 3

1 Department of Mathematics, Indiana University, Bloomington, IN, United States, Department of Mathematics, Stony Brook University, Stony Brook, NY, United States
2 Department of Mathematics, University of British Columbia, Vancouver, BC, Canada
3 Faculty of Mathematics, University of Regensburg, Regensburg, Germany, Department of Mathematical Sciences, Durham University, Durham, United Kingdom 
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Kotelskiy, Artem; Watson, Liam; Zibrowius, Claudius. A mnemonic for the Lipshitz–Ozsváth–Thurston correspondence. Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2519-2543. doi: 10.2140/agt.2023.23.2519

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