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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
Poincare 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.
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
Poincare 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.
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