# Mostly Surfaces

### About this Title

**Richard Evan Schwartz**, *Brown University, Providence, RI*

Publication: The Student Mathematical Library

Publication Year
2011: Volume 60

ISBNs: 978-0-8218-5368-9 (print); 978-1-4704-1223-4 (online)

DOI: http://dx.doi.org/10.1090/stml/060

MathSciNet review: MR2809109

MSC: Primary 57-01; Secondary 30-01, 30Fxx, 57N05

### Table of Contents

**Front/Back Matter**

**Chapters**

- Chapter 1. Book overview

**Part 1. Surfaces and topology **

- Chapter 2. Definition of a surface
- Chapter 3. The gluing construction
- Chapter 4. The fundamental group
- Chapter 5. Examples of fundamental groups
- Chapter 6. Covering spaces and the deck group
- Chapter 7. Existence of universal covers

**Part 2. Surfaces and geometry **

- Chapter 8. Euclidean geometry
- Chapter 9. Spherical geometry
- Chapter 10. Hyperbolic geometry
- Chapter 11. Riemannian metrics on surfaces
- Chapter 12. Hyperbolic surfaces

**Part 3. Surfaces and complex analysis **

- Chapter 13. A primer on complex analysis
- Chapter 14. Disk and plane rigidity
- Chapter 15. The Schwarz-Christoffel transformation
- Chapter 16. Riemann surfaces and uniformization

**Part 4. Flat cone surfaces **

- Chapter 17. Flat cone surfaces
- Chapter 18. Translation surfaces and the Veech group

**Part 5. The totality of surfaces **

- Chapter 19. Continued fractions
- Chapter 20. Teichmüller space and moduli space
- Chapter 21. Topology of Teichmüller space

**Part 6. Dessert **

- Chapter 22. The Banach–Tarski theorem
- Chapter 23. Dehn’s dissection theorem
- Chapter 24. The Cauchy rigidity theorem