In Volovik's book he describes the Fermi surface as a vortex in energy+momentum space. Due to a winding number the Fermi surface is topologically protected.
I don't understand how the above topological protection is compatible with superconductivity, which destroys the Fermi surface even for small attractive interactions. If it is a topological phase transition, there should be some type of gap closing, e.g. Fermi surface shrinking to points, which is seemingly not the case. Or is it that the pole in the Green's function still exists in a superconductor, although then I am wondering what Volovik's argument really says about the Fermi surface.
I am familiar with the terminology of Chern numbers, topological insulators etc. I would be very grateful if someone could explain this to me using that language, if possible.