Differential topology
著者
書誌事項
Differential topology
Birkhäuser , Springer, c2015
2nd ed
- : pbk
- タイトル別名
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Topics in differential topology
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注記
"Hindustan Book Agency 2005, 2nd edition 2015"--T.p. verso
"The present books is a revised version of an earlier book with the title "Topics in Differential Topology"."--P. viii
Includes bibliographical references (p. 341-343) and index
内容説明・目次
- 巻冊次
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ISBN 9783319190440
内容説明
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.
目次
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.
- 巻冊次
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: pbk ISBN 9783319369389
内容説明
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.
目次
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.
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