Local Lagrangian Floer Homology of Quasi-Minimally Degenerate Intersections

We define a broad class of local Lagrangian intersections which we call quasi-minimally degenerate (QMD) before developing techniques for studying their local Floer homology. In some cases, one may think of such intersections as modeled on minimally degenerate functions as defined by Kirwan. One major result of this paper is: if $L_0,L_1$ are two Lagrangian submanifolds whose intersection decomposes into QMD sets, there is a spectral sequence converging to their Floer homology $HF_*(L_0,L_1)$ whose $E^1$ page is obtained from local data given by the QMD pieces. The $E^1$ terms are the singular homologies of submanifolds with boundary that come from perturbations of the QMD sets. We then give some applications of these techniques towards studying affine varieties, reproducing some prior results using our more general framework.