The Smith Conjecture
Academic Press
Published on 1. May 1984
240 pages
978-0-08-087431-9 (ISBN)
Description
The Smith Conjecture
More details
Other editions
Additional editions
John W. Morgan | Hyman Bass
Smith Conjecture
Book
01/1984
Academic Press
€91.61
Article exhausted; check different version
Persons
Content
- 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
