Differential Topology

This book presents a systematic and comprehensive account of the theory of differentiable manifolds and the fundamental tools of differential topology. The text includes, in particular, the earlier works of Stephen Smale, for which he was awarded the Fields Medal. Explicitly, the topics covered are the Thom transversality, Morse theory, theory of handle presentation, h-cobordism theorem, and the generalised Poincaré conjecture. The text is the outcome of lectures and seminars on differentiable manifolds and differential topology given over the years at the Indian Statistical Institute in Calcutta, and at other universities in India.

The book will appeal to graduate students and researchers. An elementary knowledge of linear algebra, general topology, multivariate calculus, analysis, and algebraic topology is recommended.

Contents

1. Basic concepts of manifolds 1
2. Approximation theorems and whitney's embedding
3. Linear structures on manifolds
4. Riemannian manifolds
5. Vector bundles on manifolds
6. Transversality
7. Tubular neighbourhoods