Math 549, Spring 2013
1-1:50 MWF, 316 TH
Textbook: "Differential Topology" by Guillemin and Pollack
Every Monday will be a problem session/review day, please work on the exercises in the book in advance. Here is a rough guide to what will be covered each week, although this will be adjusted as needed.
- Week 1-2 : Introduction and basic definitions
- Week 3: Transversality
- Week 4: Genercity ( Sard's theorem, Morse functions, etc)
- Week 5: Whitney Embedding, Classification of 1-manifolds
- Week 6: Mod 2 Intersection theory ( Jordan Brower, Borsuk-Ulam, etc)
- Week 7: Oriented Intersection theory I (Lefschetz fixed point theorem and definitions)
- Week 8: Oriented Intersection theory II (Poincare-Hopf, degree)
- Week 7: Oriented Intersection theory III (Euler characteristics)
- Week 8: Review and midterm
- Week 9: Integration on manifolds I ( Exterior algebra, forms, integration over submanifolds )
- Week 10: Integration on manifolds II (Extrerior derivative, basics of deRham cohomology)
- Week 11: Stokes' Theorem
- Week 12: Homotopy, pull-backs
- Week 13: Gauss-Bonnet
Solutions to the first midterm.
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