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.

• h-cobordism
• handle presentations
• immersions and embeddings
• manifolds
• smooth maps
• tubular neighbourhoods transversality

“The book presented by the author consists of ten chapters. … it may serve as the first source of information on Differential Topology for all mathematics major students.” (Andrew Bucki, zbMATH 1332.57001, 2016)

• Indian Statistical Institute Statistics and Mathematics Unit, Calcutta, India

  Amiya Mukherjee

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