Three-Dimensional Geometry and Topology 1

Cover
Title page
Preface
Reader's Advisory
1 What Is a Manifold?
1.1 Polygons and Surfaces
1.2 Hyperbolic Surfaces
1.3 The Totality of Surfaces
1.4 Some Three-Manifolds
2 Hyperbolic Geometry and Its Friends
2.1 Negatively Curved Surfaces in Space
2.2 The Inversive Models
2.3 The Hyperboloid Model and the Klein Model
2.4 Some Computations in Hyperbolic Space
2.5 Hyperbolic Isometries
2.6 Complex Coordinates for Hyperbolic Three-Space
2.7 The Geometry of the Three-Sphere
3 Geometric Manifolds
3.1 Basic Definitions
3.2 Triangulations and Gluings
3.3 Geometric Structures on Manifolds
3.4 The Developing Map and Completeness
3.5 Discrete Groups
3.6 Bundles and Connections
3.7 Contact Structures
3.8 The Eight Model Geometries
3.9 Piecewise Linear Manifolds
3.10 Smoothings
4 The Structure of Discrete Groups
4.1 Groups Generated by Small Elements
4.2 Euclidean Manifolds and Crystallographic Groups
4.3 Three-Dimensional Euclidean Manifolds
4.4 Elliptic Three-Manifolds
4.5 The Thick- Thin Decomposition
4.6 Teichmüller Space
4.7 Three-Manifolds Modeled on Fibered Geometries
Glossary
Bibliography
Index