Geodesic
Heegaard Floer homology, knotifications of links, and plane curves with noncuspidal singularities
Borodzik, Maciej1 ; Liu, Beibei2 ; Zemke, Ian3
1 Institute of Mathematics, University of Warsaw, Warsaw, Poland
2 School of Mathematics, Georgia Institute of Technology, Atlanta, GA, United States, Department of Mathematics, The Ohio State University, Columbus, OH, United States
3 Department of Mathematics, Princeton University, Princeton, NJ, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 9, pp. 4837-4889

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

We describe a formula for the H1–action on the knot Floer homology of knotifications of links in S3. 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 g which cannot be topologically deformed into a genus g − 1 surface with a single double point.

DOI : 10.2140/agt.2024.24.4837
Keywords: algebraic curves, link Floer homology, knotifications of links, rational cuspidal curve

Borodzik, Maciej 1 ; Liu, Beibei 2 ; Zemke, Ian 3

1 Institute of Mathematics, University of Warsaw, Warsaw, Poland
2 School of Mathematics, Georgia Institute of Technology, Atlanta, GA, United States, Department of Mathematics, The Ohio State University, Columbus, OH, United States
3 Department of Mathematics, Princeton University, Princeton, NJ, United States 
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Borodzik, Maciej; Liu, Beibei; Zemke, Ian. Heegaard Floer homology, knotifications of links, and plane curves with noncuspidal singularities. Algebraic and Geometric Topology, Tome 24 (2024) no. 9, pp. 4837-4889. doi: 10.2140/agt.2024.24.4837

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