Cohomology of the space of generic immersion maps of surface into 3-space

In "Local Invariants of Mappings of Oriented Surfaces Into 3-Space", V.Goryunov classified singular maps of surface into 3-space and considered their resolution and local invariants.

It is natural for thinking about cohomology of the generic maps, using filtration of compactification singular sets, $$\Sigma_1^{*} \subset \Sigma_2^{*} \cdots$$ by calculating spectral sequence and using Alexander duality. Are there any results for this problem?

• There is 7 types of singularities for immersed surfaces. – this_is_a_banana Mar 10 at 10:24