Differential Topology

C. T. C. Wall (University of Liverpool)

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English

Cambridge University Press
14 July 2016

Mathematics & Sciences; Analytic topology

Series: Cambridge Studies in Advanced Mathematics

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.

By: C. T. C. Wall (University of Liverpool)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 156
Dimensions: Height: 229mm, Width: 157mm, Spine: 25mm
Weight: 640g
ISBN: 9781107153523
ISBN 10: 1107153522
Series: Cambridge Studies in Advanced Mathematics
Pages: 353
Publication Date: 14 July 2016
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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.

Reviews for Differential Topology

'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