Topological Embeddings

Name: Topological Embeddings | Topological Embeddings
Brand: Academic Press
Price: 54.95 EUR
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Ralph E. Walde(Autor*in)

Academic Press

Erschienen am 30. März 1973

315 Seiten

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978-0-08-087367-1 (ISBN)

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Inhalt

Front Cover
Topologicul Embeddings
Copyright Page
Contents
Preface
Acknowledgments
Chapter 1. Main Problem and Preliminary Notions
1.1. Introduction
1.2. Main Problem
1.3. Topological Manifolds
1.4. The Category of Polyhedra and Piecewise Linear Maps
1.5. Method of Attacking the Main Problem
1.6. Piecewise Linear Manifolds and Piecewise Linear Tools
1.7. Local Flatness, (Pinched) Collars, and (Pinched) Bicollars
1.8. Cellular Sets and Applications
Chapter 2. Wild Embeddings, Knotted Embeddings, and Related Topics
2.1. Introductory Definitions
2.2. The Group of a Knot and Knotted Codimension Two Spheres
2.3. Local Homotopy Groups, Wild Codimension Two Cells and Spheres, and Tame Nonlocally Flat Codimension Two Cells and Spheres
2.4. Wild 1-Cells, 1-Spheres, 2-Cells, and 2-Spheres in S3
2.5. En Modulo an Arc Crossed with E1 Is En+1
2.6. Everywhere Wild Cells and Spheres in En=3 of All Codimensions
2.7. Some Wild Polyhedra in Low Codimensions
Chapter 3. Flattening, Unknotting, and Taming Special Embeddings
3.1. Introduction
3.2. Almost Polyhedral Arcs Are Flat
3.3. An (n - 1)-Sphere in Sn=4 which Is Locally Flat Modulo a Point Is Flat
3.4. Flattening Cells, Half-Strings, and Strings
3.5. PL Unknotting Infinite Polyhedra in the Trivial Range
3.6. e(x)-Taming Locally Tame Embeddings of Infinite Polyhedra in The Trivial Range
3.7. e-Taming Polyhedra in the Trivial Range Which Lie in Hyperplanes
3.8. e(x) Taming Embeddings Which are Locally Tame Modulo Nice Subsets
3.9. Nonlocally Flat Points of a Codimension One Submanifold
Chapter 4. Engulfing and Applications
4.1. Introduction
4.2. Stallings' Engulfing
4.3. The Generalized Poincaré Theorem
4.4. The Hauptvermutung for Open Cells
4.5. Flattening Topological Sphere Pairs and Cell Pairs
4.6. Zeeman Engulfing
4.7. The Penrose, Whitehead, Zeeman Embedding Theorem and Irwin's Embedding Theorem
4.8. The Cellularity Criterion in High Dimensions
4.9. Locally Nice Codimension One Spheres in Sn=5 Are Weakly Flat
4.10. Radial Engulfing
4.11. The PL Approximation of Stable Homeomorphisms of En
4.12. Topological Engulfing
4.13. Topological H-Cobordisms and the Topological Poincaré Theorem
4.14. Infinite Engulfing
Chapter 5. Taming and PL Approximating Embeddings
5.1. Introduction
5.2. Cernavskii's Straightening Technique Applied to Cell Pairs and to Singular Points of Topological Embeddings
5.3. Taming Embeddings of PL Manifolds around the Boundary in All Codimensions
5.4. PL Approximating Topological Embeddings
5.5. e-Taming Allowable Embeddings of PL Manifolds
5.6. Local Contractibility of the Homeomorphism Group of a Manifold and Codimension Zero Taming
Appendix: Some Topics for Further Study
Bibliography
Author Index
Subject Index

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