Geometric Group Theory WS26
In geometric group theory, we study the interactions between groups and geometry. We view groups themselves as geometric objects or as symmetries of intereresting spaces.
We endow groups with a metric, or consider their actions on suitable metric spaces. The techniques are thus often rich in visual imagery.
Lecturer: Dr. Raphael Appenzeller
Exercise organisation: Dr. Anna Schilling
HiWi: Nils Thieme
Links: MaMpf
This lecture is classified as "Grundmodul"/"basic module".
Program
Possible topics include:
- Cayley graphs
- Free groups and trees
- Ping-Pong Lemma
- Quasi-isometries and the theorem of Milnor-Svarc
- Hyperbolic groups
- Growth of groups
- Ends of groups
Here is the course website of the same lecture held in the Winter term 2025/26: GGT Winter Semester 2025. A script by Prof. Schwer can be found here.
Pre-requisites: Basic group theory and linear algebra.
Weekly schedule
The lectures take place on Wednesday and Friday, 9:15 - 10:45 in room SR3. The first lecture is on Wednesday October 14. The exercise classes take place on Wednesday, 14:15 - 15:45 in room SR3. The first exercise class is on Wednesday October 21.
The exercise sheets appear each week on Friday afternoon and they can be submitted by Sunday the week after.
Evaluation
There will be oral exams at the end of the semester.
Attendance of the lectures and exercise classes, as well as homework submission are essential for the learning process, but there is no formal obligation to participate. Students are encouraged to work on the problem sheets and submit their work individually or in groups.
Further reading
Related things:
- A program to draw Cayley-graphs. graphicayley.de
Here are some related books:
- Bridson, M., Haefliger, A. - Metric spaces of non-positive curvature, Springer, 1999.
- Löh, C. - Geometric group theory. An introduction, Springer International Publishing, 2017. (SpringerLink)
- Bridson, M. - Geometric and combinatorial group theory. (Übersichtsartikel)
- Rosebrock, S. - Geometrische Gruppentheorie. Ein Einstieg mit dem Computer Basiswissen für Studium und Mathematikunterricht, Vieweg+Teubner Verlag, Wiesbaden, 2010. (SpringerLink)
- Stillwell, J. - Classical topology and combinatorial group theory, 2nd ed, Springer, 1993.
- Lyndon, R., Schupp, P. - Combinatorial group theory, Springer, 1977.
- Serre, J.-P. - Trees, corrected 2nd print, Springer, 2003.
