Geometry and topology of surfaces
Sommersemester 2014

Schedule

Monday and Wednesday, 9:00-11:00

INF 288, HS 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

Dr. Daniele Alessandrini, e-mail address: daniele.alessandrini@gmail.com

Office hour

Wed 15:00-16:00, Room 110, INF 288.

Exercises

We will not have regular exercise sheets every week. There will be 4-5 exercise sheets during the semester, whose solution you can optionally hand in for corrections if you wish.

Final exam

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

Content

The course is about the theory of surfaces, as developed by Thurston in the end of the 70s. The main aim is to prove Thurston's theorem of classification of homeomorphisms of surfaces up to isotopy, in principle a purely topological statement. To prove this theorem Thurston used geometric structures on surfaces, showing that geometric and topological properties are intimately related.

In the course we will introduce some geometric structures on surfaces, mainly foliations and hyperbolic structures, we will classify them and we will show how they are useful to solve the purely topological problem stated above.

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

• 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: 14/04/2014