Abstract Let be a complex analytic normal surface singularity with a rational homology sphere link . The ‘topological’ lattice cohomology associated with and with any of its structures was introduced in 34. Each is a graded ‐module. Here, we consider its homological version . The construction uses a Riemann–Roch‐type weight function. A key intermediate product is a tower of spaces such that . In this paper, we fix the embedded topological type of a reduced curve singularity embedded into a normal surface singularity , that is, a one‐dimensional link . Each component of will also carry a non‐negative integral decoration. For any fixed , the decorated embedded link provides a natural filtration of the space , which induces a homological spectral sequence converging to the homogeneous summand of the lattice homology. All the entries of all the pages of the spectral sequences are new invariants of the decorated pair . Each page provides a triple graded ‐module. We provide several concrete computations of these pages and structure theorems for the corresponding multivariable Poincaré series associated with the entries of the spectral sequences. The computations are supported by a ‘Filtered Reduction Theorem’, a reduction to the ‘bad’ vertices. The structure theorems show a surprising parallelism with Jacobi theta series.
András Némethi (Thu,) studied this question.