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Look Inside Differential Topology

Differential Topology

Part of Cambridge Studies in Advanced Mathematics

Author: C. T. C. Wall, University of Liverpool

Date Published: July 2016
availability: Available
format: Hardback
isbn: 9781107153523

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About the Authors

Exploring the full scope of differential topology, this comprehensive account of geometric techniques for studying the topology of smooth manifolds offers a wide perspective on the field. Building up from first principles, concepts of manifolds are introduced, supplemented by thorough appendices giving background on topology and homotopy theory. Deep results are then developed from these foundations through in-depth treatments of the notions of general position and transversality, proper actions of Lie groups, handles (up to the h-cobordism theorem), immersions and embeddings, concluding with the surgery procedure and cobordism theory. Fully illustrated and rigorous in its approach, little prior knowledge is assumed, and yet growing complexity is instilled throughout. This structure gives advanced students and researchers an accessible route into the wide-ranging field of differential topology.
- Addresses a wide range of results in differential topology using an integrated and unified approach
- Requires little prior knowledge, with thorough appendices providing relevant background
- Includes recent results, making it up to date and relevant for current researchers
- Fully illustrated to provide additional explanation and context
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Reviews & endorsements
'The book is of the highest quality as far as scholarship and exposition are concerned, which fits with the fact that Wall is a very big player in this game. I have had occasion over the years to do a good deal of work from books in the Cambridge Studies in Advanced Mathematics Series, always top drawer productions, and the present volume is no exception. I very much look forward to making good use of this fine book.' Michael Berg, MAA Reviews
'This monograph by the famous topologist C. T. C. Wall is based on his mimeographed notes from the 1960s. These notes are amended and supplemented with some new material, but they retain the spirit of the time when dfferential topology was still new and there were no books on the subject. This makes for a comprehensive yet highly readable introduction to the subject which has the right balance of intuition and rigor and which does not shy away from explaining 'well-known' facts.' Nikolai N. Saveliev, Mathematical Reviews
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Product details
- Date Published: July 2016
- format: Hardback
- isbn: 9781107153523
- length: 353 pages
- dimensions: 229 x 157 x 25 mm
- weight: 0.64kg
- contains: 30 b/w illus.
- availability: Available
Table of Contents
Introduction
1. Foundations
2. Geometrical tools
3. Differentiable group actions
4. General position and transversality
5. Theory of handle decompositions
6. Immersions and embeddings
7. Surgery
8. Cobordism
Appendix A. Topology
Appendix B. Homotopy theory
References
Index of notation
Index.
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Author
C. T. C. Wall, University of Liverpool
C. T. C. Wall is Emeritus Professor in the Division of Pure Mathematics at the University of Liverpool. During his career he has held positions at the University of Oxford and the University of Cambridge and has been invited as a major speaker to numerous conferences in Europe, the USA and South America. He was elected a Fellow of the Royal Society in 1969.