Topology and Analysis II. See Chapters 3 (Implicit Function Theorem), 4 (Flow of Vector Fields) and Appendices A,B,C (Basic Topology) of these German lecture notes: here. For topology, you can also see the standard reference by Munkres.
Lecture Notes will be updated over the semester. The most up to date version can be found here. If you spot any typos, please communicate these to the lecturer.
Submanifolds of \(\mathbb{R}^n\), tangent bundle, embeddings and immersions, vector fields, Lie bracket, Frobenius' Theorem. Geodesics, exponential map, completeness, Hopf-Rinow. Levi-Civita connection, parallel transport, motions without twisting, sliding, and wobbling. Isometries, Riemann curvature, Theorema Egregium. Cartan-Ambrose-Hicks, symmetric spaces, constant curvature, Hadamard's theorem.
The new exercises will be posted here on Tuesday. We expect you to look at the problems before exercise class and to prepare questions for the exercise class on Thursday/Friday.
If you want to hand in your solutions, please do so by the following Monday at 14:00 in your assistant's box in HG F28. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG F28. Note that model solutions will be provided.
If you spot any mistakes or typos in the exercises or solutions, please communicate these to the coordinators.
| exercise sheet | due by | solutions |
|---|---|---|
| Exercise sheet 1 | September 25 | Solutions 1 |
| Exercise sheet 2 | October 2 | Solutions 2 |
| Exercise sheet 3 | October 9 | Solutions 3 |
| Exercise sheet 4 | October 16 | Solutions 4 |
| Exercise sheet 5 | October 23 | Solutions 5 |
| Exercise sheet 6 | October 30 | Solutions 6 |
| Exercise sheet 7 | November 6 | Solutions 7 |
| Exercise sheet 8 | November 13 | Solutions 8 |
| Exercise sheet 9 | November 20 | Solutions 9 |
| Exercise sheet 10 | November 27 | Solutions 10 |
| Exercise sheet 11 | December 4 | Solutions 11 |
| Exercise sheet 12 | December 11 | Solutions 12 |
| Exercise sheet 13 | December 18 | Solutions 13 |
| Exercise sheet 14 | Merry Christmas and a Happy New Year :) |
Please sign up to an exercise class on echo ( echo.ethz.ch ).
| time | room | assistant | language |
|---|---|---|---|
| Th 14-15 | HG D 5.2 | Charel Antony | en |
| Th 14-15 | HG E 21 | Samuel Trautwein | en |
| Th 15-16 | HG D 7.2 | Charel Antony | en |
| Fr 13-14 | HG G 26.3 | Samuel Trautwein | en |
We will add books here that complement the material in class.