MATH 758: Topics in Topology (Spring 2007)

Instructor: Peter Kahn

Meeting Time & Room

Morse theory studies differentiable manifolds, both finite and infinite dimensional, by slicing them up according to the level surfaces of some nice height function or energy function. This has been a fundamental tool in both algebraic and differental topology, leading to the Morse homology and Floer homology theories. The latter has played an important role in symplectic topology and in recent work on low-dimensional manifolds. In this course, we'll follow the book, Morse Homology by Augustin Banyaga, which covers the classical theory as well as Morse and Floer homology. Another (perhaps supplementary) text is Milnor's Morse Theory.

Last modified:October 31, 2006