Math 690: Morse Theory and its Applications,
Fall 2021, Syllabus
Latest COVID-19 information
In this classs we will be studying
Morse Theory and
its applications.
Here is a preliminary plan for the course:
- Morse functions
-
- The local structure of Morse functions
- Existence of Morse functions
- The topology of Morse functions
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- Surgery, handle attachments and cobordism
- The topology of sublevel sets
- Morse inequalities
- Morse-Smale dynamics
- Morse-Floer homology
- Morse-Bott functions
- Applications
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- Complex Grassmannians
- Lefschetz hyperplane theorems
- Bott periodicity theorem
- Witten deformation
- Homotopy groups of BDiff(Sn)
- Generalized Morse functions
- H-principle for generalized Morse functions
Reading for the class:
There will be 4 homework assignments and (possibly) home-take exam.
More information to come
Last modified September 26, 2021 by
Boris Botvinnik.