Table of contents for Algebraic and geometric surgery / Andrew Ranicki.


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1  The surgery classification of manifolds                       1

2  Manifolds                                                           14
   2.1  Differentiable manifolds                                      14
   2.2  Surgery                                                       16
   2.3  Morse theory                                                  18
   2.4  Handles                                                       22

3  Homotopy and homology                                               29
   3.1  Homotopy                                                      29
   3.2  Homology                                                      33

4  Poincare duality                                                    48
   4.1  Poincare duality                                              48
   4.2  The homotopy and homology effects of surgery                  53
   4.3  Surfaces                                                      61
   4.4  Rings with involution                                         66
   4.5  Universal Poincar6 duality                                    72

5  Bundles                                                             86
   5.1  Fibre bundles and fibrations                                  86
   5.2  Vector bundles                                                89
   5.3  The tangent and normal bundles                               105
   5.4  Surgery and bundles                                          112
   5.5  The Hopf invariant and the J-homomorphism                    118

6  Cobordism theory                                                  124
   6.1  Cobordism and transversality                                 124
   6.2  Framed cobordism                                             129
   6.3  Unoriented and oriented cobordism                            133
   6.4  Signature                                                    135




7  Embeddings, immersions, and singularities                         142
         The Whitney Immersion and Embedding Theorems               142
         Algebraic and geometric intersections                      148
         The Whitney trick                                          156
         The Smale-Hirsch classification of immersions              161
         Singularities                                              167

8  Whitehead torsion                                                 170
         The Whitehead group                                        170
         The h- and s-Cobordism Theorems                            175
         Lens spaces                                                186

9  Poincare complexes and spherical fibrations                       193
         Geometric Poincare complexes                               194
         Spherical fibrations                                       198
         The Spivak normal fibration                                205
         Browder-Novikov theory                                     209

10 Surgery on maps                                                   218
         Surgery on normal maps                                     220
         The regular homotopy groups                                226
         Kernels                                                    231
         Surgery below the middle dimension                         239
         Finite generation                                          241

11 The even-dimensional surgery obstruction                          247
         Quadratic forms                                            247
         The kernel form                                            256
         Surgery on forms                                           282
         The even-dimensional L-groups                              289
         The even-dimensional surgery obstruction                   296

12 The odd-dimensional surgery obstruction                           302
         Quadratic formations                                       302
         The kernel formation                                       307
         The odd-dimensional L-groups                               317
         The odd-dimensional surgery obstruction                    320
         Surgery on formations                                      323
         Linking forms                                              334



13 The structure set                                                    340
    13.1 The structure set                                              340
    13.2 The simple structure set                                       344
    13.3 Exotic spheres                                                 346
    13.4 Surgery obstruction theory                                     356

References                                                              361

Index                                                                   367





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