Author(s): T.B. Rushing
Series: Pure and Applied Mathematics, A Series of Monographs and Textbooks
Year: 1973
Language: English
Pages: 316
Front Cover......Page 1
Topologicul Embeddings......Page 4
Copyright Page......Page 5
Contents......Page 8
Preface......Page 12
Acknowledgments......Page 14
1.2. Main Problem......Page 16
1.3. Topological Manifolds......Page 17
1.4. The Category of Polyhedra and Piecewise Linear Maps......Page 19
1.5. Method of Attacking the Main Problem......Page 23
1.6. Piecewise Linear Manifolds and Piecewise Linear Tools......Page 24
1.7. Local Flatness, (Pinched) Collars, and (Pinched) Bicollars......Page 48
1.8. Cellular Sets and Applications......Page 59
2.2. The Group of a Knot and Knotted Codimension Two Spheres......Page 66
2.3. Local Homotopy Groups, Wild Codimension Two Cells and Spheres, and Tame Nonlocally Flat Codimension Two Cells and Spheres......Page 71
2.4. Wild 1-Cells, 1-Spheres, 2-Cells, and 2-Spheres in S3......Page 75
2.5. En Modulo an Arc Crossed with E1 Is En+1......Page 89
2.6. Everywhere Wild Cells and Spheres in En≥3 of All Codimensions......Page 99
2.7. Some Wild Polyhedra in Low Codimensions......Page 106
3.1. Introduction......Page 113
3.2. Almost Polyhedral Arcs Are Flat......Page 114
3.3. An (n - 1)-Sphere in Sn≥4 which Is Locally Flat Modulo a Point Is Flat......Page 115
3.4. Flattening Cells, Half-Strings, and Strings......Page 120
3.5. PL Unknotting Infinite Polyhedra in the Trivial Range......Page 125
3.6. ε(x)-Taming Locally Tame Embeddings of Infinite Polyhedra in The Trivial Range......Page 133
3.7. ε-Taming Polyhedra in the Trivial Range Which Lie in Hyperplanes......Page 147
3.8. ε(x) Taming Embeddings Which are Locally Tame Modulo Nice Subsets......Page 149
3.9. Nonlocally Flat Points of a Codimension One Submanifold......Page 151
4.1. Introduction......Page 163
4.2. Stallings’ Engulfing......Page 164
4.3. The Generalized Poincaré Theorem......Page 168
4.4. The Hauptvermutung for Open Cells......Page 169
4.5. Flattening Topological Sphere Pairs and Cell Pairs......Page 173
4.6. Zeeman Engulfing......Page 181
4.7. The Penrose, Whitehead, Zeeman Embedding Theorem and Irwin’s Embedding Theorem......Page 185
4.8. The Cellularity Criterion in High Dimensions......Page 193
4.9. Locally Nice Codimension One Spheres in Sn≥5 Are Weakly Flat......Page 198
4.10. Radial Engulfing......Page 200
4.11. The PL Approximation of Stable Homeomorphisms of En......Page 208
4.12. Topological Engulfing......Page 215
4.13. Topological H-Cobordisms and the Topological Poincaré Theorem......Page 221
4.14. Infinite Engulfing......Page 229
5.1. Introduction......Page 235
5.2. Černavskiĭ’s Straightening Technique Applied to Cell Pairs and to Singular Points of Topological Embeddings......Page 236
5.3. Taming Embeddings of PL Manifolds around the Boundary in All Codimensions......Page 256
5.4. PL Approximating Topological Embeddings......Page 264
5.5. ε-Taming Allowable Embeddings of PL Manifolds......Page 274
5.6. Local Contractibility of the Homeomorphism Group of a Manifold and Codimension Zero Taming......Page 285
Appendix: Some Topics for Further Study......Page 309
Bibliography......Page 311
Author Index......Page 324
Subject Index......Page 327
