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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

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Table of Contents

Front/Back Matter

• View this volume's front and 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

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