By: Northeastern University
Introduces the topology of complex hypersurfaces and their singularities. Begins with the geometric content of the complex implicit function theorem, and moves quickly to the study of the Milnor fibration of a hypersurface singularity. Uses Brieskorn varieties and plane curves as fundamental examples of isolated singularities. The study of nonisolated singularities, such as the Whitney umbrella and discriminantal varieties, requires stratification theory. Covers the basics of stratified Morse theory and uses it as a tool throughout the course. The course supposes a certain familiarity with the basic objects of topology, algebra, and geometry, but reviews necessary notions as the need arises.