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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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 17 Oct 2019