Articoli correlati a Geometry on Poincare Spaces
Sinossi
A Poincaré space is a topological space satisfying Poincaré duality, as a compact manifold. This book explains how to perform, in the category of Poincaré spaces, a certain number of geometric constructions which are usual in the world of manifolds (surgery, handle techniques, transversality, etc.). These constructions turn out to be useful in solving manifold problems, such as embeddings and group actions. This is the first book to be published on this subject. The methods are based on standard surgery theory and elementary homotopy arguments.
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Contenuti
| Introduction | 1 | |
| 1 | Homology Theories Over RP[actual symbol not reproducible] | |
| A | The category over RP [actual symbol not reproducible] | 9 |
| B | Homology with local coefficients | 11 |
| C | Homology theories over RP[actual symbol not reproducible] with coefficients in a module | 14 |
| D | Examples | 19 |
| E | Cap-products - The Hurewicz homomorphism | 21 |
| F | Other homology theories over RP[actual symbol not reproducible] | 23 |
| 2 | Poincare Duality - Basic Properties | |
| A | PD-Spaces | 25 |
| B | PD-Decompositions | 30 |
| C | Smoothing low-dimensional skeleta | 39 |
| 3 | Q-Spaces - Poincare Spaces | |
| A | A homology theory over BG | 58 |
| B | Q-Spaces | 62 |
| C | Poincare spaces | 73 |
| D | Poincare surgeries: preliminaries | 77 |
| 4 | The Poincare Bordism Groups and the Exact Sequence of Quinn | |
| A | Presentation of the results | 85 |
| B | Proof of Proposition (4.7) | 94 |
| C | Proof of Proposition (4.8) | 106 |
| 5 | Surgery on Poincare Spaces | |
| A | The formal point of view | 142 |
| B | Manifold engulfings | 152 |
| C | The geometric point of view | 161 |
| 6 | Handle Decompositions for Poincare Spaces | 167 |
| 7 | The Obstruction to Transversality | |
| A | Transversality up to Poincare bordism | 174 |
| B | Transversality up to homotopy equivalence | 189 |
| 8 | The Quinn Exact Sequence for Other Kinds of Poincare Spaces | |
| A | Simple Poincare spaces | 211 |
| B | A-Poincare spaces | 212 |
| C | Non-finite Poincare spaces | 229 |
| 9 | Other Applications | 236 |
| Appendix: On Fibrations with Complexes Having Finite Skeleta | 242 | |
| References | 245 | |
| Index | 251 |
Product Description
Book by Hausmann JeanClaude Vogel Pierre
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Geometry on Poincare Spaces (Mathematical Notes 41)
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