Semigroups,d-invariants and deformations of cuspidal singular points of plane curves

We study δ-constant deformations of plane curve singularities from a topological point of view. We introduce a topological counterpart to a δ-constant deformation in singularity theory. Methods from Heegaard Floer theory give a purely topological proof of the semicontinuity property for semigroups of singular points of plane curves under δ-constant deformation. Using the same approach, we also give a knot-theoretical result concerning minimal unknotting sequences of torus knots. To conclude, we describe generalizations to arbitrary knots.