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The Shape of Space
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Table of Contents

Part I Surfaces and Three-Manifolds

Flatland

Gluing

Vocabulary

Orientability

Classification of Surfaces

Products

Flat Manifolds

Orientability vs. Two-Sidedness

Part II Geometries on Surfaces

The Sphere

The Hyperbolic Plane

Geometries on Surfaces

Gauss-Bonnet Formula and Euler Number

Part III Geometries on Three-Manifolds

Four-Dimensional Space

The Hypersphere

Hyperbolic Space

Geometries on Three-Manifolds I

Bundles

Geometries on Three-Manifolds II

Part IV The Universe

The Universe

The History of Space

Appendix A: Answers

Appendix B: Bibliography

Appendix C: Conway’s ZIP Proof

About the Author

Jeffrey R. Weeks is a free-lance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and—closest to his heart—exposition for the general public.

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