MAU34304 Groups and geometry
| Module Code | MAU34304 |
|---|---|
| Module Title | Groups and geometry |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Tommaso Cremaschi |
| Module Prerequisites |
MAU11100 Linear algebra and
MAU22101 Group theory and MAU23203 Analysis in several real variables |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 10% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Apply basic theorems on discrete subgroups of isometries.
- Build examples of discrete groups acting on different geometric spaces.
- Classify wallpaper groups.
Module Content
The aim of this module is to study the isometry groups of various metric spaces such as real euclidean n-space, spherical n-space, and hyperbolic n-space with an emphasis on their discrete subgroups. As an example of topics, we will look at crystallographic/wallpaper groups, Bieberbach theorem, Schottky groups and the ping-pong Lemma.