Contents Forewords ix Editor's foreword to the second edition xi Introduction xv Part 0: Preliminaries Note on conventions 2 0. Basic homotopy notions 3 1. Surgery below the middle dimension 8 1A. Appendix: applications 17 2. Simple Poincare complexes 21 Part 1: The main theorem 3. Statement of results 32 4. An important special case 39 5. The even-dimensional case 44 6. The odd-dimensional case 57 7. The bounded odd-dimensional case 74 8. The bounded even-dimensional case 82 9. Completion of the proof 91 Part 2: Patterns of application 10. Manifold structures on Poincare complexes 106 11. Applications to submanifolds 118 12. Submanifolds: other techniques 138 12A. Separating submanifolds 142 12B. Two-sided submanifolds 149 12C. One-sided submanifolds 155 Part 3: Calculations and applications 13A. Calculations: surgery obstruction groups 172 13B. Calculations: the surgery obstructions 185 14. Applications: free actions on spheres 195 14A. General remarks 195 14B. An extension of the Atiyah-Singer G-signature theorem 199 14C. Free actions of S1 202 14D. Fake projective spaces (real) 206 14E Fake lens spaces 213 15. Applications: free uniform actions on euclidean space 231 15A. Fake tori 232 15B. Polycyclic groups 237 16. Applications to 4-manifolds 241 vii
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