Morse Theory and Floer Homology 2022

Instructor: Matt Carr.

(Tentative) Syllabus: Morse functions, Morse lemma, stable and unstable manifolds, cellular decomposition of manifolds, the handle presentation theorem, spaces of broken flow lines and Morse homology. Lightning review of basic symplectic topology and real analysis; discussion of transversality and smooth function spaces. Construction of Floer homology (or as much as we can get through). Comparison with Morse homology. Vistas.

Schedule: We will have three lectures per week, on Mondays, Wednesdays, and Fridays, from 11 a.m. to 12:30 p.m., starting on June 6th, and ending on June 24th, in room MW154. Click here for the Zoom link to attend virtually.


Due to an injury that I incurred in the course of these lectures, I am unhappy with the quality of the remaining lectures and will be re-recording these.

Main reference: The following are the main references for this course.

  • Audin and Damian’s Morse Theory and Floer Homology.
  • Lecture notes (still in progress). They include a refresher on tools and concepts from analysis we will need, built from notes I took in 2016.

Extra references: The following are extra references some of which I will be using and others I will not be using.

  • Milnor’s Morse Theory
    • This is the other standard reference but Milnor goes off in a direction we will not pursue.
  • Kosinksi’s Differential Manifolds.
    • This is the presentation we will follow when discussing the handle presentation theorem.
  • Golubitsky and Guillemin’s  Stable mappings and their singularities.
    • Our very own Golubitsky.
  • Peter Michor’s Manifolds of Differentiable Mappings.
    • Covers some of the same ground as the above.
  • Hirsch’s Differential Topology.
    • One should be aware this has errors in some arguments. These are addressed in other references.
  • Ivo Terek’s lecture notes A Guide to Symplectic Geometry.
  • Oh’s Symplectic Topology and Floer Homology.
    • Much more than we can possibly discuss, including Lagrangian Floer homology.