Introduction to Manifolds, Aug-Nov 2015
Vijay Ravikumar (vijayr at cmi dot ac dot in)
Tuesday and Thursday 11:50 - 13:05
CMI Lecture Hall 3
(Transition Mapping by Lun-Yi Tsai)
(Transition Mapping by Lun-Yi Tsai)
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 4 (tue) | 1: smooth functions on Euclidean space | |
| Aug 6 (thu) | 2: tangent vectors in Euclidean space | |
| Aug 11 (tue) | 3: some multilinear algebra | |
| Aug 13 (thu) | 4: differential forms on Euclidean space | homework #1 due |
| Aug 18 (tue) | 5: manifolds | |
| Aug 20 (thu) | 6: smooth maps | homework #2 due |
| Aug 25 (tue) | 7: quotients; the differential of a map | |
| Aug 27 (thu) | 8: more about the differential | homework #3 due |
| Sep 1 (tue) | 9: submanifolds | |
| Sep 3 (thu) | 10: the rank of a smooth map | homework #4 due |
| Sep 8 (tue) | 11: vector bundles | |
| Sep 10 (thu) | 12: vector fields | homework #5 due |
| Sep 15 (tue) | 13: partitions of unity, embedding theorems | |
| Sep 17 (thu) | HOLIDAY (Vinayaka Chathurthi) | |
| Sep 22 (tue) | MIDTERM EXAM WEEK | |
| Sep 24 (thu) | MIDTERM EXAM WEEK | |
| Sep 29 (tue) | 14: lie groups | |
| Oct 1 (thu) | 15: lie algebras | |
| Oct 6 (tue) | 16: differential 1-forms | |
| Oct 8 (thu) | 17: k-forms and riemannian metrics | homework #7 due |
| Oct 13 (tue) | 18: the exterior derivative | |
| Oct 15 (thu) | 19: the lie derivative, interior multiplication | homework #8 due |
| Oct 20 (tue) | 20: orientations, manifolds with boundary | |
| Oct 22 (thu) | HOLIDAY (Vijaya Dasami) | |
| Oct 27 (tue) | 21: integration on manifolds | |
| Oct 29 (thu) | 22: de rham cohomology | homework #9 due |
| Nov 3 (tue) | 23: the mayer-vietoris sequence | |
| Nov 5 (thu) | 24: some cohomology computations | homework #10 due |
| Nov 10 (tue) | HOLIDAY (Deepavali) | |
| Nov 12 (thu) | 25: proof of homotopy invariance | |
| Nov 17 (tue) | 26: intro to morse theory, classical viewpoint | |
| Nov 19 (thu) | 27: intro to morse theory, modern viewpoint | homework #11 due |
| Nov 24 (tue) | FINAL EXAM WEEK | |
| Nov 26 (thu) | FINAL EXAM WEEK |
(Hopf Fibration by Lun-Yi Tsai)