Math 378, Stratified Morse Theory

Spring 2012

This will be an introduction to and survey of the Stratified Morse Theory developed by Goresky and MacPherson. The standard reference is their book, Stratified Morse Theory, (Ergebnisse vol. 14, Springer-Verlag, 1989), which has excellent expository chapters and contains full details of all proofs. You can obtain a copy (in djvu format, which can be viewed using djview) from Mark Goresky's web page.

The course will be a survey. I will focus on how to use SMT. I'll begin with a quick review of classical Morse theory, with an emphasis on its applications to the topology of complex algebraic varieties. Some topics I hope to cover include:

• Whitney stratified spaces
• stratified Morse functions
• normal slices and links
• Morse data and the fundamental theorem
• complex links
• Lefschetz type theorems

1. Goresky, Mark; MacPherson, Robert: Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 14, Springer-Verlag, 1988
2. Milnor, J.: Morse theory, Annals of Mathematics Studies, No. 51 Princeton University Press, 1963

Handouts:

• Notes on the Morse theory of complex manifolds: (pdf)