Heegaard Floer homology and plane curves with non-cuspidal singularities

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.

40 pages. Minor revision

References in corpus (2)

• Chern-Simons functional, singular instantons, and the four-dimensional clasp number
• A note on the four-dimensional clasp number of knots