The Smith Conjecture

Name: The Smith Conjecture
Brand: Academic Press
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Academic Press

Erschienen am 1. Mai 1984

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Inhalt

Front Cover
The Smith Conjecture, Volume 112
Copyright Page
Contents
Contributors
Preface
Acknowledgments
List of Notation
PART A: INTRODUCTION
Chapter 1. The Smith Conjecture
1. Formulations
2. Generalizations
3. Some Consequences Relating to the Poincaré Conjecture
4. Additional Remarks
Chapter 2. History of the Smith Conjecture and Early Progress
1. History of the Smith Conjecture
2. Early Progress
Chapter 3. An Outline of the Proof
1. Preliminaries
2. First Reductions
3. The Argument in Brief
References for Part A
PART B: THE CASE OF NO INCOMPRESSIBLE SURFACE
Chapter 4. The Proof in the Case of No Incompressible Surface
Introduction
1. The Algebraic Approach to the Smith Conjecture
2. Hyperbolic Geometry and Algebraic Integers
3. The Existence of Hyperbolic Structures and the Torus Theorem
4. PSL2(C) and Incompressible Surfaces
5. History
References
Chapter 5. On Thurston's Uniformization Theorem for Three-Dimensional Manifolds
Introduction
1. An Introduction to Hyperbolic Geometry
2. Kleinian Groups
3. Statement of the Main Theorem-The Case of Finite Volume
4. Hierarchies and Pared Manifolds
5. Statement of the Main Theorem-The General Case
6. Convex Hyperbolic Structures of Finite Volume
7. The Gluing Theorem-Statement and First Reduction
8. Combination Theorems
9. Deformation Theory
10. The Fixed Point Theorem
11. The First Step in the Proof of the Bounded Image Theorem
12. Completion of the Proof of the Bounded Image Theorem
13. Special Cases
14. Kleinian Groups with Torsion
15. Patterns of Circles
16. The Inductive Step in the Proof of Theorems A' and B'
References
Chapter 6. Finitely Generated Subgroups of GL2
1. The GL2-Subgroup Theorem
2. Arboreal Group Theory
3. The Tree of SL2 over a Local Field
4. Proof of the GL2-Subgroup Theorem
References
PART C: THE CASE OF AN INCOMPRESSIBLE SURFACE
Chapter 7. Incompressible Surfaces in Branched Coverings
1. Introduction
2. Terminology and Statement of Results
3. Proofs of Theorems 1 and 2
4. The Equivalent Loop Theorem for Involutions
References
Chapter 8. The Equivariant Loop Theorem for Three-Dimensional Manifolds and a Review of the Existence Theorems for Minimal Surfaces
1. Morrey's Solution for the Plateau Problem in a General Riemannian Manifold
2. The Existence Theorem for Manifolds with Boundary
3. Existence of Closed Minimal Surfaces
4. Existence of the Free Boundary Value Problem for Minimal Surfaces
References
PART D: GENERALIZATIONS
Chapter 9. Group Actions on R3
References
Chapter 10. Finite Group Actions on Homotopy 3-Spheres
1. Orbifolds
2. Two-Dimensional Orbifolds
3. Three-Dimensional Orbifolds
4. Seifert-Fibered Orbifolds
5. Seifert-Fibered Orbifolds and Linear Actions
6. Statement of the Main Results
7. A Special Case
8. Completion of the Proof
Appendix
References
Chapter 11. A Survey of Results in Higher Dimensions
1. The Montgomery-Samuelson Example
2. G-Complexes
3. The Brieskorn Examples
4. Oliver's Example
5. Local Properties: Groups of Homeomorphisms versus Groups of Diffeomorphisms
6. Work of Lowell Jones
7. Actions on Disks
8. Actions on Spheres
9. Actions on Euclidean Spaces
References
Index

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