Introduction to Manifolds, Aug-Nov 2016
Vijay Ravikumar (vijayr at cmi dot ac dot in)
Monday 10:30 - 11:45 / Friday 9:10 - 10:35
CMI Lecture Hall 1 / 2
(by Anatoly Fomenko)
(by Anatoly Fomenko)
1) Late homework will be accepted at half credit until exactly one week after the due date. No homework will be accepted after that point.
2) If you have difficulty with an assignment, you are encouraged to approach the instructor for help. It is also fine to discuss the problems with other students, but...
3) Your final write-up must be your own. If you have received help solving a problem, then you must cite your source(s). In particular, plagiarism, or any kind of copying, will not be tolerated. Offences will result in serious disciplinary action, up to and including a failing grade in the course.
| date | lecture # | announcements |
| Aug 1 (mon) | 1: smooth functions on Euclidean space | |
| Aug 3 (wed) | 2: tangent vectors in Euclidean space | |
| Aug 8 (mon) | 3: some multilinear algebra | |
| Aug 10 (wed) | 4: more multilinear algebra | homework #1 due |
| Aug 12 (fri) | 5: the exterior derivative | |
| Aug 19 (fri) | 6: manifolds | homework #2 due |
| Aug 22 (mon) | 7: smooth maps | |
| Aug 26 (fri) | 8: the jacobian and the differential | |
| Aug 29 (mon) | 9: the tangent space | homework #3 due |
| Sep 2 (fri) | 10: submanifolds | |
| Sep 7 (wed) | 11: regular level sets | |
| Sep 9 (fri) | 12: rank of a smooth map | homework #4 due |
| Sep 12 (mon) | 13: vector bundles | |
| Sep 16 (fri) | 14:vector fields | homework #5 due |
| Sep 19 (mon) | MIDTERM EXAM WEEK | |
| Sep 23 (fri) | MIDTERM EXAM WEEK | |
| Sep 26 (mon) | 15: partitions of unity | |
| Sep 30 (fri) | 16: flows, lie bracket | |
| Oct 3 (mon) | 17: lie groups | |
| Oct 7 (fri) | 18: tangent space at identity | homework #6 due |
| Oct 14 (fri) | 19: lie algebras | |
| Oct 17 (mon) | 20: lie group actions | homework #7 due |
| Oct 19 (wed) | 21: quotients of manifolds by group actions | |
| Oct 21 (fri) | 22: differential forms | |
| Oct 24 (mon) | 23: exterior derivative | |
| Oct 28 (fri) | 24: lie derivative and contraction | |
| Oct 31 (mon) | 25: orientations on manifolds | homework #8 due |
| Nov 2 (wed) | 26: manifolds with boundary | |
| Nov 4 (fri) | 27: integration | |
| Nov 7 (mon) | 28: de rham cohomology | homework #9 due |
| Nov 9 (wed) | 29: the mayer-vietoris sequence | |
| Nov 11 (fri) | 30: some cohomology computations | |
| Nov 14 (mon) | 31: proof of homotopy invariance | homework #10 due |
| Nov 17 (thu) | FINAL EXAM |
(by Anatoly Fomenko)