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Heegaard Floer
homology, knotifications of links, and plane curves with
noncuspidal singularities
Maciej Borodzik, Beibei Liu and Ian Zemke |
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Algebraic & Geometric Topology 24 (2024) 4837–4889
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Abstract |
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We describe a formula for the –action on the knot Floer homology of knotifications of links in . Using our results about knotifications, we are able to study complex curves with noncuspidal singularities, which were inaccessible using previous Heegaard Floer techniques. We focus on the case of a transverse double point, and give examples of complex curves of genus which cannot be topologically deformed into a genus surface with a single double point. |
Keywords
algebraic curves, link Floer homology, knotifications of
links, rational cuspidal curve
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Mathematical Subject Classification
Primary: 14H50
Secondary: 14B05, 57K18, 57R58
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References |
Publication
Received: 27 February 2022
Revised: 16 September 2022
Accepted: 1 February 2023
Published: 27 December 2024
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Authors |
| Maciej Borodzik | |
| Institute of Mathematics University of Warsaw Warsaw Poland |
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| Beibei Liu | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
Department of Mathematics The Ohio State University Columbus, OH United States |
| Ian Zemke | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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