Three-dimensional Orbifolds and Cone-Manifolds

Description

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. 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