The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it.
The topics included in the course are:
Prerequisites are topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester.
Exercise classes take place on the following dates (replacing the lecture):
Exercises will be given continuously throughout the course, and the students should work on them regularly. The above dates are for more involved explanations and questions. Small questions can be asked at any time during or after the lecture.
The exercises will be uploaded on this page. Some of the exercises will be discussed in the following exercise class.
| Exercise sheet | Lecture notes | Hints or partial solutions |
|---|---|---|
| Exercise sheet 1 | Notes week 1: Lecture 1 & 2 | Partial solutions 1 |
| Exercise sheet 2 | Notes week 2: Lecture 1, Lecture 2 | Partial solutions 2 |
| Exercise sheet 3 | Notes week 3: Lecture 1, Lecture 2 | Partial solutions 3 |
| Notes week 4: Lecture 1, Lecture 2 | ||
| Week 5: exercise classes | ||
| Exercise sheet 4 | Notes week 6: Lecture 1 & 2 | Partial solutions 4 |
| Exercise sheet 5 |
Notes week 7: Lecture 1 & 2
Notes from Boothby's book Introduction to Differentiable Manifolds and Riemannian Geometry Theorem 7.8 / Proposition 3.43 |
Partial solutions 5 |
| Exercise sheet 6 | Notes week 8: Lecture 1 & 2 | Partial solutions 6 |
| Week 9: exercise classes | ||
| Exercise sheet 7 | Notes week 10: Lecture 1 & 2 | Partial solutions 7 |
| Exercise sheet 8 | Notes week 11: Lecture 1 & 2 | Partial solutions 8 |
| Exercise sheet 9 | Notes week 12: Lecture 1, Lecture 2 | Partial solutions 9 |
| Week 13: exercise classes | ||
| Notes week 14: Lecture 1 & 2 |
The course will basically follow Alessandra Iozzi's notes From topological groups to Lie groups, which are still in revision.