Differential Topology

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 Front Matter....Pages i-xiii Basic Concepts of Manifolds....Pages 1-42 Approximation Theorems and Whitney’s Embedding....Pages 43-67 Linear Structures on Manifolds....Pages 69-104 Riemannian Manifolds....Pages 105-131 Vector Bundles on Manifolds....Pages 133-167 Transversality....Pages 169-198 Tubular Neighbourhoods....Pages 199-223 Spaces of Smooth Maps....Pages 225-265 Morse Theory....Pages 267-298 Theory of Handle Presentations....Pages 299-340 Back Matter....Pages 341-349