Spring 2005 : MAT 595 From Morse homology to Floer homology

Tuesday and Thursday 12:00-1:20 in Henry 152

Overview of the course

Floer theory, which combines ideas from Morse theory and the study of pseudoholomorphic curves, is one of the central tools in modern symplectic topology. The goal of this course will be to describe the ideas and technical issues involved in Floer theory and to discuss some recent applications. We will spend at least the first third of the course discussing Morse homology which is a beautiful topic itself and serves as an illuminating finite-dimensional prototype of Floer homology.

Below is link to some old lecture notes from a previous incarnation of this course. I will be revising these notes throughout the semester.

  • LECTURE NOTES

    Prerequisites

    I hope to make this course accessible to anyone with a good knowledge of basic differential topology.

    Office Hours

    My office is room 331 in Illini Hall and my official office hours for this course will be Wednesday 2-4. Unofficially, you are welcome to come to my office to discuss the material whenever you have questions.

    References

    We will not follow a particular book, but here are two very useful sets of lecture notes which are available on the web:

  • "Lecture notes on Morse homology (with an eye towards theory and pseudoholomorphic curves)" by Michael Hutchings, http://math.berkeley.edu/~hutching.

  • "Lectures on Floer homology" by Dietmar Salamon, http://math.ethz.ch/%7Esalamon/publications.html.

    Here are some other excellent references.

    For Morse homology:

  • "Morse homology" by Matthias Schwarz (Birkhauser PM 111).
  • Chapter 6 of "Riemannian geometry and geometric analysis, Third Edition" by Jurgen Jost.

    For the "classical" approach to Morse theory:

  • "Morse theory" by John Milnor.
  • "An introduction to Morse theory" by Yukio Matsumoto.

    For pseudoholomorphic curves and Floer theory:

  • "J-holomorphic curves and quantum cohomology" by Dusa McDuff and Dietmar Salamon.
  • "The Floer memorial volume" (Birkhauser PM 133).
  • The papers of M. Schwarz in "Contact and Symplectic Geometry", edited by C.B. Thomas (Cambridge University Press).

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    This page last modified by Ely Kerman
    Friday, 20-Jan-2005 13:12:53 EST
    Email corrections and comments to ekerman@math.uiuc.edu