Algebraic and Geometric Surgery

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Clarendon Press, 2002 - Mathematics - 373 pages
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'An excellent framework for various courses in Surgery Theory... very readable... I read this fine and carefully written book with great pleasure, and highly recommend it for everyone who wants to undertake a deeper study of Surgery Theory and its Applications.' -Alberto Cavicchioli (Modena), Zentralblatt MATHThis 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.
 

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Contents

The surgery classification of manifolds
1
Manifolds
14
Homotopy and homology
29
Poincare duality
48
Bundles
86
Cobordism theory
124
Embeddings immersions and singularities
142
Whitehead torsion
170
g Poincare complexes and spherical fibrations
193
Surgery on maps
218
The evendimensional surgery obstruction
247
The odddimensional surgery obstruction
302
The structure set
340
References
361
Index
367
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About the author (2002)

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

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