UID:
almafu_9958066805202883
Format:
1 online resource (263 p.)
ISBN:
1-281-76871-5
,
9786611768713
,
0-08-087431-2
Series Statement:
Pure and applied mathematics ; 112
Content:
The Smith conjecture
Note:
Description based upon print version of record.
,
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
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Chapter 4. The Proof in the Case of No Incompressible SurfaceIntroduction; 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
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5. Statement of the Main Theorem-The General Case6. 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
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3. The Tree of SL2 over a Local Field4. 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
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2. The Existence Theorem for Manifolds with Boundary3. 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
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Chapter 11. A Survey of Results in Higher Dimensions
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English
Additional Edition:
ISBN 0-12-506980-4
Language:
English
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