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?

  • $\begingroup$ There is 7 types of singularities for immersed surfaces. $\endgroup$ – this_is_a_banana Mar 10 '19 at 10:24

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