Algebraic and Geometric Surgery

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Andrew Ranicki (, Department of Mathematics and Statistics, University of Edinburgh)

Algebraic and Geometric Surgery

Andrew Ranicki (, Department of Mathematics and Statistics, University of Edinburgh)

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English

Oxford University Press
01 October 2002

Algebra; Algebraic geometry; Analytic topology

Series: Oxford Mathematical Monographs

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.

By: Andrew Ranicki ( Department of Mathematics and Statistics University of Edinburgh)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 242mm, Width: 162mm, Spine: 25mm
Weight: 672g
ISBN: 9780198509240
ISBN 10: 0198509243
Series: Oxford Mathematical Monographs
Pages: 386
Publication Date: 01 October 2002
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

Reviews for Algebraic and Geometric Surgery

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 MATH