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A
mnemonic for the Lipshitz–Ozsváth–Thurston correspondence
Artem Kotelskiy, Liam Watson and Claudius Zibrowius |
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Algebraic & Geometric Topology 23 (2023) 2519–2543
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Abstract |
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When is a field, type D structures over the algebra are equivalent to immersed curves decorated with local systems in the twice-punctured disk. Consequently, knot Floer homology, as a type D structure over , can be viewed as a set of immersed curves. With this observation as a starting point, given a knot in , we realize the immersed curve invariant 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 in terms of the knot Floer homology of . |
Keywords
Fukaya categories of punctured surfaces, bordered Heegaard
Floer theory, multicurve invariants, knot Floer homology
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Mathematical Subject Classification
Primary: 57K18, 57K31
Secondary: 57R58
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References |
Publication
Received: 30 July 2020
Revised: 8 October 2021
Accepted: 11 February 2022
Published: 7 September 2023
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Authors |
| Artem Kotelskiy | |
| Department of Mathematics Indiana University Bloomington, IN United States |
Department of Mathematics Stony Brook University Stony Brook, NY United States |
| https://artofkot.github.io/ | |
| Liam Watson | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| https://personal.math.ubc.ca/~liam/ | |
| Claudius Zibrowius | |
| Faculty of Mathematics University of Regensburg Regensburg Germany |
Department of Mathematical
Sciences Durham University Durham United Kingdom |
| https://cbz20.raspberryip.com/ | |
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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