代数的および幾何的手術 Algebraic and Geometric Surgery (Oxford Mathematical Monographs)

Ranicki, Andrew

Clarendon Press（2002/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 386 p.
• 言語 ENG
• 商品コード 9780198509240
• DDC分類 514.72

基本説明

Provides an introduction to surgery theory; the standard classification method for high dimension manifolds.

Full Description

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 contains entry-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 on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.

Contents

Preface ; 1. The surgery classification of manifolds ; 2. Manifolds ; 3. Homotopy and homology ; 4. Poincare duality ; 5. Bundles ; 6. Cobordism theory ; 7. Embeddings, immersions and singularities ; 8. Whitehead torsion ; 9. Poincare complexes and spherical fibrations ; 10. Surgery on maps ; 11. The even-dimensional surgery obstruction ; 12. The odd-dimensional surgery obstruction ; 13. The structure set ; References ; Index