Morse theory for plane curves

I develop a tool for studying plane algebraic curves. It consists on intersecting a given plane curve C with spheres S(z,r), centered at some point z and radius r. For almost all r, this intersection is some link in the sphere. I can control the change of isotopy type of the link when crossing a nontransversality point. The change of some classical invariants of the links gives some restriction on the topology and geometry of C. The lecture will be self-contained and accessible for non-specialists in the theory of plane curves.