Math392C: Morse Theory

Announcements

I adjusted the schedule of student lectures for October and into November. Let me know if there are any issues.

Basic Information

Professor: Dan Freed

Class Meetings: W 4:00-7:00, RLM 9.166

Discusion/Office Hours: M 2:30-4:00, RLM 9.162

For more details, see the First Day Handout

Schedule

Topic/Reference Student(s) Date
Existence of Morse functions Max Riestenberg September 5
Kenny Schefers
Handles and handlebodies Riccardo Pedrotti September 12
George Torres
Knots and total curvature Jonathan Johnson September 26
Sebastian Schulz
Lefschetz hyperplane theorem Ivan Tulli October 3
Ricky Wedeen
Milnor, Chapters 4 and 5 Riccardo Pedrotti October 10
Cameron Darwin
Milnor, Chapter 5 Cameron Darwin October 17
Milnor, Chapter 6 Gill Grindstaff October 24
Ricky Wedeen
Milnor, Chapter 7 Tynan Ochse October 31
Charlie Reid
Milnor, Chapters 8 and 9 Kenny Schefers November 7
Arun Debray


Notes

Note on the deformation retraction argument in the September 12 lecture.

Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4

Problem Set #5

Problem Set #6

Problem Set #7

Problem Set #8

Problem Set #9

Problem Set #10

Problem Set #11

Readings

Morse survey on critical point theory.

Milnor essay on differential topology.

Bott's Morse Theory indomitable.

Moser's paper proving Darboux's theorem.

Jost on Morse homology (from his book Riemannian Geometry and Geometric Analysis).

Michael Hutching's class notes on Morse homology.

Smale's infinite dimensional version of Sard's theorem.

Donaldson-Kronheimer discussion of transversality.

Schwarz appendix from Morse Homology on Banach manifolds of paths and vector bundles over them.

Smale paper on gradient dynamical systems.

Cohen-Jones-Segal preprint on Morse theory and classifying spaces.