UID:
almafu_9958115644102883
Format:
1 online resource (333 p.)
ISBN:
1-281-98411-6
,
9786611984113
,
0-08-087367-7
Series Statement:
Pure and applied mathematics : a series of monographs and textbooks ; v. 52
Content:
Topological embeddings
Note:
Includes indexes.
,
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
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2.2. The Group of a Knot and Knotted Codimension Two Spheres2.3. 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
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3.3. An (n - 1)-Sphere in Sn=4 which Is Locally Flat Modulo a Point Is Flat3.4. 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
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4.4. The Hauptvermutung for Open Cells4.5. 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
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5.2. Cernavskii's Straightening Technique Applied to Cell Pairs and to Singular Points of Topological Embeddings5.3. 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
,
English
Additional Edition:
ISBN 0-12-603550-4
Language:
English
