Lattice Cohomology of Normal Surface Singularities

András Némethi

Source: Publ. Res. Inst. Math. Sci. Volume 44, Number 2 (2008), 507-543.

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 is discussed in the light of this new object.

Primary Subjects: 4B05, 14J17, 32S25, 57M27, 57R57

Secondary Subjects: 14E15, 32S45, 57M25

Keywords: normal surface singularities; line bundles; geometric genus; rational singularities; elliptic singularities; almost rational singularities; Seiberg-Witten invariant; Heegaard-Floer homology; Seiberg-Witten Invariant Conjecture

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Permanent link to this document: http://projecteuclid.org/euclid.prims/1210167336
Digital Object Identifier: doi:10.2977/prims/1210167336

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