Analytic lattice cohomology of surface singularities, II (the equivariant case)

2021/08/27 by Tamás Ágoston, András Némethi, Ágoston, Tamás +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2108.12429

Abstract

We construct the equivariant analytic lattice cohomology associated with the analytic type of a complex normal surface singularity whenever the link is a rational homology sphere. It is the categorification of the equivariant geometric genus of the germ. This is the analytic analogue of the topological lattice cohomology, associated with the link of the germ, and indexed by the spin^c--structures of the link (which is a categorification of the Seiberg--Witten invariant and conjecturally it is isomorphic with the Heegaard Floer cohomology).

Related

• Analytic lattice cohomology of surface singularities
• The analytic lattice cohomology of isolated singularities
• Lattice cohomology of normal surface singularities
• The geometric genus of hypersurface singularities
• Lattice cohomology and the embedded topological type of plane curve singularities