
Algebraic and Geometric Surgery
Andrew Ranicki(Author)
Oxford University Press
Published on 26. September 2002
Book
Hardback
386 pages
978-0-19-850924-0 (ISBN)
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.
Reviews / Votes
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 *More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Illustrations
numerous line figures
Dimensions
Height: 242 mm
Width: 162 mm
Thickness: 25 mm
Weight
672 gr
ISBN-13
978-0-19-850924-0 (9780198509240)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Content
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