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MATH 6240 - Differential Geometry 2 - Fall 2017
Class Schedule
The following schedule is tentative and incomplete, and will be modified throughout the term.
| Week | Dates | Topics | Reading | Notes |
|---|---|---|---|---|
| 1 | Aug 28 - Sept 1 | review, vector bundles | Lee Chapter 1-2 | |
| 2 | Sept 6-8 | Riemannian metrics | Lee Chapter 3 | Monday is Labor Day (no classes)! |
| 3 | Sept 11-15 | connections | Lee Chapter 4 | |
| 4 | Sept 18-22 | geodesics | Lee Chapter 5 | |
| 5 | Sept 25-29 | exponential map, normal neighbourhoods, completeness | Lee Chapter 6 | |
| 6 | Oct 2-6 | curvature | Lee Chapter 7 | |
| 7 | Oct 9-13 | Riemannian submanifolds | Lee Chapter 8 | |
| 8 | Oct 16-20 | Gauss-Bonnet Theorem | Lee Chapter 9 | |
| 9 | Oct 23-27 | Jacobi fields | Lee Chapter 10 | |
| 10 | Oct 30 - Nov 3 | positive/negative/constant curvature | Lee Chapter 11 | |
| 11 | Nov 6-10 | principal bundles | Roe, Berline-Getzler-Vergne | |
| 12 | Nov 13-17 | characteristic classes | Roe, Berline-Getzler-Vergne,Kobayashi-Nomizu | |
| Fall & Thanksgiving Breaks | ||||
| 13 | Nov 27 - Dec 1 | Clifford algebras, Dirac operators, and spin structures | Roe | |
| 14 | Dec 4-8 | Fredholm operators, Dirac operators are Fredholm | Roe | |
| 15 | Dec 11-13 | asymptotic expansions, Lefschetz formula, index theorems | Roe | |