Contents ix Chapter 6. Codimension-two Embeddings 273 §6.1. Piecewise linear knotting and algebraic unknotting 274 §6.2. Topological flattening and algebraic knotting 283 §6.3. Local flatness and local homotopy properties 293 §6.4. The homology of an infinite cyclic cover 298 §6.5. Properties of the Alexander polynomial 311 §6.6. A topological embedding that cannot be approximated by PL embeddings 325 §6.7. A homotopy equivalence that is not homotopic to an embedding 334 §6.8. Disk bundle neighborhoods and taming 346 Chapter 7. Codimension-one Embeddings 349 §7.1. Codimension-one separation properties 350 §7.2. The 1-LCC characterization of local flatness for collared embeddings 353 §7.3. Unknotting close 1-LCC embeddings of manifolds 358 §7.4. The Cell-like Approximation Theorem 366 §7.5. Determining n-cells by embeddings of Mn n−1 in Sn 371 §7.6. The 1-LCC characterization of local flatness 377 §7.7. Locally flat approximations 382 §7.8. Kirby-Siebenmann obstruction theory 402 §7.9. Detecting 1-LCC embeddings 403 §7.10. Sewings of crumpled n-cubes 410 §7.11. Wild examples and mapping cylinder neighborhoods 417 Chapter 8. Codimension-zero Embeddings 425 §8.1. Manifold characterizations 425 §8.2. The α- and β-Approximation Theorems 427 §8.3. Ends of manifolds 427 §8.4. Ends of maps 432 §8.5. Quinn’s obstruction and the topological characterization of manifolds 435 §8.6. Exotic homology manifolds 437 §8.7. Homotopy tori are tori 439 §8.8. Approximating stable homeomorphisms of Rn by PL homeomorphisms 439
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