Three-dimensional Orbifolds and Cone-Manifolds

✍ Scribed by Daryl Cooper, Craig D. Hodgson, Steven P. Kerckhoff

• Publisher: The Mathematical Society of Japan
• Year: 2000
• Tongue: English
• Leaves: 177
• Series: Mathematical Society of Japan Memoirs, Volume 5
• Category: Library

✦ Synopsis

This volume provides an excellent introduction of the statement and main ideas in the proof of the orbifold theorem announced by Thurston in late 1981. It is based on the authors' lecture series entitled "Geometric Structures on 3-Dimensional Orbifolds" which was featured in the third MSJ Regional Workshop on "Cone-Manifolds and Hyperbolic Geometry" held on July 1-10, 1998, at Tokyo Institute of Technology. The orbifold theorem shows the existence of geometric structures on many 3-orbifolds and on 3-manifolds with symmetry. The authors develop the basic properties of orbifolds and cone-manifolds, extends many ideas from the differential geometry to the setting of cone-manifolds and outlines a proof of the orbifold theorem.

✦ Table of Contents

Title and Copyright Pages
Preface
Table of Contents
Introduction
Chapter 1. Geometric Structures
Chapter 2. Orbifolds
Chapter 3. Cone-Manifolds
Chapter 4. Two-dimensional Cone-Manifolds
Chapter 5. Deformations of Hyperbolic Structures
Chapter 6. Limits of Metrics Spaces
Chapter 7. Proof of the Orbifold Theorem
Background on the Orbifold Theorem
Bibliography
Index
Postface.pdf