Contents Acknowledgments xi Introduction: The Main Problem xiii Chapter 0. Prequel 1 §0.1. More definitions and notation 1 §0.2. The Seifert-van Kampen Theorem 3 §0.3. The ultimate duality theorem 6 §0.4. The Vietoris-Begle Theorem 9 §0.5. Higher homotopy groups 9 §0.6. Absolute neighborhood retracts 12 §0.7. Dimension theory 14 §0.8. The Hurewicz Isomorphism Theorem and its localization 16 §0.9. The Whitehead Theorem 17 §0.10. Acyclic complexes and contractible manifolds 17 §0.11. The 2-dimensional PL Sch¨ onflies Theorem 19 Chapter 1. Tame and Knotted Embeddings 23 §1.1. Knotted and flat piecewise linear embeddings 23 §1.2. Tame and locally flat topological embeddings 29 §1.3. Local co-connectedness properties 30 §1.4. Suspending and spinning 35 vii
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