# Themen der Geometrie

Sommersemester 2015

### Schedule

Tuesday and Thursday, 11:00-13:00

INF 288, HS 3

The course will start on Tuesday May 5.

### Müsli

There is a page for this course on MÜSLI.

Even if there are no exercise groups, please, register on MÜSLI, in this way you can receive communications about the course.

### Contact

### Office hour

Will be announced soon.### Exercises

Here is a collection of exercises related with the material of the course.

### Final exam

There will be a final exam at the end of the course (end of July).

### Content

The course will be about the Thurston-Teichmüller theory, the study of the geometry of hyperbolic surfaces. This theory can be studied from several different points of view: the point of view of Riemannian geometry, studying Riemannian metrics of constant curvature -1 on the surface; the point of view of complex geometry, studying the theory of Riemann surfaces; and the point of view of representations, studying discrete and injective group homomorphisms of the fundamental group of the surface in the group PSL(2,R). The main object of study will be the Teichmüller space, the parameter space of each of the aforementioned objects.

This course is a good opportunity to learn the basics of geometric topology and low dimensional topology starting from the simplest example (surfaces), understand how geometric and topological properties are related, apply tools already learned in calculus classes to geometric problems.

### References

- Buser :
*Geometry and spectra of compact Riemann surfaces*. - Series :
*Hyperbolic Geometry*. - Hubbard :
*Teichmueller theory*. - Fathi, Laudenbach, Poénaru :
*Thurston's Work on Surfaces*. - Farb, Margalit :
*A primer on mapping class groups*. - Thurston :
*Three dimensional geometry and topology, vol. 1*. - Benedetti, Petronio :
*Lectures on hyperbolic geometry*.

Last modified: 03/07/2015