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Hyperbolic Geometry (Winter 2019-2020)
Contents
Course description
This is an introductory course on hyperbolic geometry. Both the lectures and exercise sessions are taught by myself in English.
Contents will include:
- Introduction to non-Euclidean geometry and curvature
- Minkowski geometry and the hyperboloid model
- Projective geometry and the Klein model
- Conformal geometry and the Poincaré models
- Hyperbolic trigonometry
- Möbius transformations, \(\mathbb{H}^2\) and \(\mathbb{H}^3\)
- Gromov hyperbolic spaces and classification of isometries
- Hyperbolic manifolds (time permits)
Prerequisites
No prerequisites are required, but the more geometry you studied, the easier the course will be.
References
I will not base the lectures on one reference in particular. I suggest you do your own research to find references that you like. I can personally recommend the following:
- Ratcliffe's book Foundations of hyperbolic manifolds is a great reference for learning hyperbolic geometry for the first time and for future reference. It is very well written and self-contained.
- Thurston's book Three-dimensional geometry and topology is not specifically about hyperbolic geometry, but it is a great idea to read it regardless because it is a beautiful introduction to many geometric ideas. Chapter 2 provides an introduction to hyperbolic geometry.
- If you want to learn Riemannian geometry, which is not required for this course but nevertheless a good idea, I find that Lee's Riemannian manifolds is a very good textbook for first-time learners. A new edition came out in 2018.
Exam
Ask me in person.
Class time and location & Office hours
Lectures: Thursdays 15:20-17:00, room 301 or 409K in S2|15 (see schedule)
Exercise sessions: Fridays 15:20-17:00 (approximately every other week, see schedule), room 234 in S2|15
Office hours: By appointment
Note that the Lectures and Exercise sessions have been interchanged!
NB: Refer to the course schedule below for the precise dates.
Lecture notes and Exercise sheets (PDF)
Hyperbolic geometry is an introductory book to hyperbolic geometry based on a course taught at TU Darmstadt in the winter 2019-2020. Download (PDF).
Click on the exercise sheets below to view or download.
Course schedule
NB: The course schedule below is subject to updates.
| Date | Subject | Location | Remarks |
|---|---|---|---|
| Fri. 18.10.2019 | Lecture #1 (Chap 1, Chap 2) | S2|15 234 | |
| Thu. 24.10.2019 | Lecture #2 (Chap 2) | S2|15 409K | |
| Thu. 31.10.2019 | Lecture #3 (Chap 3) | S2|15 409K | |
| Fri. 01.11.2019 | Exercise session #1 | S2|15 234 | |
| Thu. 07.11.2019 | Lecture #4 (Chap 4) | S2|15 409K | |
| Fri. 08.11.2019 | Lecture #5 (Chap 4) | S2|15 234 | Exceptional date |
| Thu. 14.11.2019 | Lecture #6 (Chap 5) | S2|15 301 | |
| Fri. 15.11.2019 | Exercise session #2 | S2|15 234 | |
| Thu. 21.11.2019 | - | - | Cancelled: moved to 08.11 |
| Thu. 28.11.2019 | Lecture #7 (Chap 5) | S2|15 409K | |
| Fri. 29.11.2019 | Exercise session #3 | S2|15 234 | |
| Thu. 05.12.2019 | Lecture #8 (Chap. 6) | S2|15 301 | |
| Thu. 12.12.2019 | Lecture #9 (Chap. 6) | S2|15 301 | |
| Fri. 13.12.2019 | Exercise session #4 | S2|15 234 | |
| Thu. 19.12.2019 | Lecture #10 (Chap. 7) | S2|15 301 | |
| Thu. 16.01.2020 | Lecture #11 (Chap. 7) | S2|15 301 | |
| Fri. 17.01.2020 | Exercise session #5 | S2|15 234 | |
| Thu. 23.01.2020 | Lecture #12 (Chap. 8) | S2|15 301 | |
| Thu. 30.01.2020 | Lecture #13 (Chap. 9) | S2|15 409K | |
| Fri. 31.01.2020 | Exercise session #6 | S2|15 234 | |
| Thu. 06.02.2020 | Lecture #14 (Chap. 10) | S2|15 301 | |
| Thu. 13.02.2020 | Lecture #15 (Chap. 11) | S2|15 301 | |
| Fri. 14.02.2020 | Exercise session #7 | S2|15 234 |