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Algebraic and Geometric Surgery (Oxford Mathematical Monographs)

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Synopses & Reviews

Publisher Comments:

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, co-bordism, 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.

Book News Annotation:

Surgery theory is a general method for the classification of manifolds. This book aims to be an entry point to surgery theory for readers with some background in topology. The prerequisites of both the algebraic and the geometric parts of surgery are presented here, and enough machinery is developed to prove the main result of the theory. Coverage progresses from manifolds, homotopy and homology, and Poincar<'e> duality through even- and odd-dimensional surgery obstruction and the structure set. Ranicki teaches in the Department of Mathematics and Statistics at the University of Edinburgh. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Includes bibliographical references (p. [361]-365) and index.

Table of Contents

Preface

1. The surgery classification of manifolds

2. Manifolds

3. Homotopy and homology

4. Poincaré duality

5. Bundles

6. Cobordism theory

7. Embeddings, immersions and singularities

8. Whitehead torsion

9. Poincaré 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

Product Details

ISBN:
9780198509240
Author:
Ranicki, Andrew
Publisher:
Oxford University Press
Location:
Oxford
Subject:
Topology
Subject:
Surgery (Topology)
Subject:
Topology - General
Subject:
Mathematics | Pure Mathematics
Subject:
MATHEMATICS / Topology
Series:
Oxford mathematical monographs
Series Volume:
No. 495
Publication Date:
20030131
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
69 line illus
Pages:
392
Dimensions:
6.4 x 9.3 x 1 in 1.46 lb

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Algebraic and Geometric Surgery (Oxford Mathematical Monographs) New Hardcover
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Product details 392 pages Oxford University Press - English 9780198509240 Reviews:
"Synopsis" by , Includes bibliographical references (p. [361]-365) and index.
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