Differential Topology (2^nd Ed., Softcover reprint of the original 2nd ed. 2015)

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

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

Preface.- 1.Basic Concepts of Manifolds.- 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.- 8.Spaces of Smooth Maps.- 9.Morse Theory.- 10.Theory of Handle Presentations.- Bibliography.- Index. 

Introduces the fundamental tools of differential topology

Ideally suited as a textbook for an orientation course for advanced-level research students or for independent study

Presents a number of epochal discoveries in the field of manifolds

Includes supplementary material: sn.pub/extras