MA 306: Topics in Morse Theory

Credits: 3:0

Prerequisite courses: MA 232, MA 338

Pre-requisites :

1. Manifolds and submanifolds
2. critical points, Sard’s theorem
3. vector fields as differential equations
4. Riemannian metrics, exponential map."

Transversality, Morse functions, stable and unstable manifolds, Morse-Smale moduli spaces, the space of gradient flows, compactification of the moduli spaces of flows, Morse homology, applications.

Suggested books and references:

1. Michèle Audin, Mihai Damian, Morse Theory and Floer Homology, 2014, Springer-Verlag London.
2. J. Milnor, Morse Theory, Ann. of Math. Stud. 51, Princeton Univ. Press, Princeton, 1963..
3. L. Nicolescu, An invitation to Morse theory, http://www3.nd.edu/~lnicolae/Morse2nd.pdf.
4. M. Schwarz, Morse homology, Birkhäuser, Basel, 1993.
5. R. Cohen, Kevin Iga, Paul Norbury, Topics in morse theory, lecture notes, 2006.

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