Differential Topology

A comprehensive account giving advanced students and researchers an accessible route into the wide-ranging field of differential topology.

C. T. C. Wall (Author)

9781107153523, Cambridge University Press

Hardback, published 4 July 2016

353 pages, 30 b/w illus.
22.9 x 15.7 x 2.5 cm, 0.64 kg

'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

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.

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.

Subject Areas: Topology [PBP], Geometry [PBM], Mathematics [PB]