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. © 2008 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.