Algebraic and Geometry Surgery

Oxford Mathematical Monographs

Andrew Ranicki

374 pages, parution le 12/12/2002

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Résumé

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 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

L'auteur - Andrew Ranicki

Department of Mathematics and Statistics, University of Edinburgh

Caractéristiques techniques

	PAPIER
Éditeur(s)	Oxford University Press
Auteur(s)	Andrew Ranicki
Parution	12/12/2002
Nb. de pages	374
Format	16 x 24
Couverture	Relié
Poids	665g
Intérieur	Noir et Blanc
EAN13	9780198509240
ISBN13	978-0-19-850924-0