Lattice cohomology and the embedded topological type of plane curve singularities

Analytic lattice cohomology is a new invariant of reduced curve singularities. In the case of plane curves, it is an algebro-geometric analogue of Heegaard Floer Link homology. However, by the rigidity of the analytic structure, lattice cohomology can be naturally defined in higher codimensions as well. In this paper we show that in the case of irreducible plane curve singularities the lattice cohomology is a complete embedded topological invariant. We also compare it to the integral Seifert form in the case of multiple branches.