Cohomology of contact loci

We construct a spectral sequence converging to the cohomology with compact support of m-th contact locus complex polynomial. The first page is explicitly described in terms log resolution and coincides McLean’s Floer $m$‑th iterate monodromy, when polynomial has an isolated singularity. Inspired by this connection, we conjecture that if two germs holomorphic functions are embedded topologically equivalent, then Milnor fibers their tangent cones homotopy equivalent.