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Mostly Surfaces
Richard Evan Schwartz
Table of Contents
- Book overview
- Definition of a surface
- The gluing construction
- The fundamental group
- Examples of fundamental groups
- Covering spaces and the deck group
- Existence of universal covers
- Euclidean geometry
- Spherical geometry
- Hyperbolic geometry
- Riemann metrics on surfaces
- Hyperbolic surfaces
- A primer on complex analysis
- Disk and plane rigidity
- The Schwarz-Christoffel transformation
- Riemann surfaces and uniformization
- Flat cone surfaces
- Translation surfaces and the Veech group
- Continued fractions
- Teichmüller space and moduli space
- Topology of Teichmüller space
- The Banach Tarski theorem
- Dehn's dissection theorem
- The Cauchy rigidity theorem
- Bibliography
- Index