Contents
Preface xi
Chapter 1. Book Overview 1
§1.1. Behold, the Torus! 1
§1.2. Gluing Polygons 3
§1.3. Drawing on a Surface 5
§1.4. Covering Spaces 8
§1.5. Hyperbolic Geometry and the Octagon 9
§1.6. Complex Analysis and Riemann Surfaces 11
§1.7. Cone Surfaces and Translation Surfaces 13
§1.8. The Modular Group and the Veech Group 14
§1.9. Moduli Space 16
§1.10. Dessert 17
Part 1. Surfaces and Topology
Chapter 2. Definition of a Surface 21
§2.1. A Word about Sets 21
§2.2. Metric Spaces 22
§2.3. Open and Closed Sets 23
§2.4. Continuous Maps 24
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