| Description |
1 online resource (xi, 373 pages) : illustrations |
| Series |
Oxford mathematical monographs |
|
Oxford science publications |
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Oxford mathematical monographs.
|
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Oxford science publications.
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| Contents |
1. The surgery classification of manifolds -- 2. Manifolds -- 2.1. Differentiable manifolds -- 2.2. Surgery -- 2.3. Morse theory -- 2.4. Handles -- 3. Homotopy and homology -- 3.1. Homotopy -- 3.2. Homology -- 4. Poincare duality -- 4.1. Poincare duality -- 4.2. The homotopy and homology effects of surgery -- 4.3. Surfaces -- 4.4. Rings with involution -- 4.5. Universal Poincare duality -- 5. Bundles -- 5.1. Fibre bundles and fibrations -- 5.2. Vector bundles -- 5.3. The tangent and normal bundles -- 5.4. Surgery and bundles -- 5.5. The Hopf invariant and the J-homomorphism -- 6. Cobordism theory -- 6.1. Cobordism and transversality -- 6.2. Framed cobordism -- 6.3. Unoriented and oriented cobordism -- 6.4. Signature -- 7. Embeddings, immersions, and singularities -- 7.1. The Whitney Immersion and Embedding Theorems |
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7.2. Algebraic and geometric intersections -- 7.3. The Whitney trick -- 7.4. The Smale-Hirsch classification of immersions -- 7.5. Singularities -- 8. Whitehead torsion -- 8.1. The Whitehead group -- 8.2. The h- and s-Cobordism Theorems -- 8.3. Lens spaces -- 9. Poincare complexes and spherical fibrations -- 9.1. Geometric Poincare complexes -- 9.2. Spherical fibrations -- 9.3. The Spivak normal fibration -- 9.4. Browder-Novikov theory -- 10. Surgery on maps -- 10.1. Surgery on normal maps -- 10.2. The regular homotopy groups -- 10.3. Kernels -- 10.4. Surgery below the middle dimension -- 10.5. Finite generation -- 11. The even-dimensional surgery obstruction -- 11.1. Quadratic forms -- 11.2. The kernel form -- 11.3. Surgery on forms -- 11.4. The even-dimensional L-groups -- 11.5. The even-dimensional surgery obstruction |
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12. The old-dimensional surgery obstruction -- 12.1. Quadratic formations -- 12.2. The kernel formation -- 12.3. The odd-dimensional L-groups -- 12.4. The odd-dimensional surgery obstruction -- 12.5. Surgery on formations -- 12.6. Linking forms -- 13. The structure set -- 13.1. The structure set -- 13.2. The simple structure set -- 13.3. Exotic spheres -- 13.4. Surgery obstruction theory |
| Summary |
An introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds |
| Bibliography |
Includes bibliographical references (pages 361-365) and index |
| Notes |
Print version record |
| Subject |
Surgery (Topology)
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MATHEMATICS -- Topology.
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Surgery (Topology)
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| Form |
Electronic book
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| Author |
Oxford University Press
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| ISBN |
9780191545245 |
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0191545244 |
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9780191708725 |
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0191708720 |
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