Modul

The module will be completed by an oral exam (of ca. 20 - 30 min).

At the end of the course, students

• have a deeper understanding of the topology and geometry of surfaces, as well as of the structure of their homeomorphisms;
• are able to work independently and critically;
• are prepared to read recent research articles and work on a thesis on mapping class groups and related topics.

None

• curves on surfaces up to homotopy and isotopy,
• mapping class groups of surfaces,
• Nielsen-Thurston classification of homeomorphisms of surfaces,
• Teichmüller space.

The contents of the courses 'Introduction into Geometry and Topology' and 'Elementary Geometry' are recommended. The courses 'Hyperbolic Geometry' and 'Algebraic Topology' can faciliate a deeper understanding of the course contents.

Total workload: 90 hours

Attendance: 30 hours

•  lectures and examination

Self-studies: 60 hours

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research relating to the course content,
• preparation for the module examination