Algebraic and Geometric Surgery

Hardcover | September 15, 2002

byAndrew Ranicki

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This book is 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. This text containsentry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, cobordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating onthe basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.

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This book is 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. This text containsentry-level accounts of the various prerequisit...

Andrew Ranicki is at the Department of Mathematics and Statistics, University of Edinburgh.

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Format:HardcoverDimensions:386 pages, 9.21 × 6.14 × 0.99 inPublished:September 15, 2002Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198509243

ISBN - 13:9780198509240

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Table of Contents

Preface1. The surgery classification of manifolds2. Manifolds3. Homotopy and homology4. Poincare duality5. Bundles6. Cobordism theory7. Embeddings, immersions and singularities8. Whitehead torsion9. Poincare complexes and spherical fibrations10. Surgery on maps11. The even-dimensional surgery obstruction12. The odd-dimensional surgery obstruction13. The structure setReferencesIndex