Lattice Cohomology of Normal Surface Singularities

Abstract

For any negative definite plumbed 3-manifold $M$ we construct from its plumbed graph a graded $Z[U]$-module. This, for rational homology spheres, conjecturally equals the Heegaard–Floer homology of Ozsváth and Szabó, but it has even more structure. If $M$ is a complex singularity link then the normalized Euler-characteristic can be compared with the analytic invariants. The Seiberg–Witten Invariant Conjecture of [16], [13] is discussed in the light of this new object.