Heegaard Floer homology and plane curves with non-cuspidal singularities

Maciej Borodzik; Beibei Liu; Ian Zemke

doi:10.2140/agt.2024.24.4837

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arXiv · 2104.13709

Heegaard Floer homology and plane curves with non-cuspidal singularities

Maciej Borodzik·Beibei Liu·Ian Zemke

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Abstract

We study possible configurations of singular points occuring on general algebraic curves in $\mathbb{C}P^2$ via Floer theory. To achieve this, we describe a general formula for the $H_{1}$-action on the knot Floer complex of the knotification of a link in $S^3$, in terms of natural actions on the link Floer complex of the original link. This result may be interest on its own.

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Maciej Borodzik, Beibei Liu, Ian Zemke. 2021-04-28. Heegaard Floer homology and plane curves with non-cuspidal singularities. https://doi.org/10.2140/agt.2024.24.4837

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