# Riemann Surfaces and Mapping Class Groups

*When and where:* Sunday 15:15-17:00 Room 155 Ziskind Building (On Sunday 3/11 the lesson is moved to Room 208 Goldsmith Building. There will be no lesson on Sunday 29/12/19 and 05/01/20).

A tentative synopsis can be found on the course page of the FGS.

### Lecture notes

These are the notes that I wrote. Comments are always welcome.

- Chapter 1: Planar Domains (v2.1)
- Chapter 2: Structures on surfaces (v2)
- Chapter 3: Riemann surfaces (v2)
- Chapter 4: Topology and geometry of surfaces (v1.1)
- Chapter 5: Teichmüller and Thurston (v1.1)

### Exercises

These are the problem sheets. You do not have to solve all the exercises.

- Exercises - Week 1
- Exercises - Week 2
- Exercises - Week 3
- Exercises - Week 4
- Exercises - Week 5
- Exercises - Week 6
- Exercises - Week 7
- Exercises - Week 8
- Exercises - Week 9
- Exercises - Week 10
- Exercises - Week 11
- Exercises - Week 12 - End Projects

### Some extra material

These are some extra notes that you might find useful. They are not going to be mentioned in class.

- Planar differential geometry. Here we introduce a few more ideas of Riemannian geometry in the context of planar domains.

### References

These are some books and papers that I found useful while preparing this course:

- (Recommended)H.M. Farkas, I. Kra:
*Riemann Surfaces*. Springer (1980) - W. Rudin:
*Real and complex analysis*. McGraw-Hill (1986) - (Recommended)B. Martelli:
*An Introduction to Geometric Topology*. Independent Publication (2016) - L. Ahlfors, L. Sario:
*Riemann Surfaces*. Princeton University press (1960) - H. Zieschang, E. Vogt, H.D. Coldewey:
*Surfaces and Planar Discontinuous Groups*. Springer (1980) - (Recommended)B. Farb, D. Margalit:
*A primer on mapping class groups*. Princeton University press (2012) - H. Cartan:
*Elementary Theory of Analytic Functions of One or Several Complex Variables*Dover Books in Mathematics (1973). - F. Bonahon:
*The geometry of Teichmiiller space via geodesic currents*. Invent. Math.**92**,139-162 (1988) - W. Thurston (S. Levy edit.):
*Three-Dimensional Geometry and Topology*. Princeton University Press (1997) - W. Thurston:
*The Geometry and Topology of Three-Manifolds*. Lecture notes - M. do Carmo:
*Differential Geometry of Curves and Surfaces*. Prentice-Hall (1976) - S. Gallot, D. Hulin, J. Lafontaine:
*Riemannian Geometry*. Springer (1987) - E. Moise:
*Geometric Topology in Dimensions 2 and 3*. Springer (1977) - M. Spivak:
*A comprehensive introduction to Differential Geometry*. Publish or Perish, 3rd Edition (1999) - A. Hatcher
*Algebraic topology*. Cambridge University Press (2002) pdf

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