Differential topology

書誌事項

Differential topology

Amiya Mukherjee

Birkhäuser , Springer, c2015

2nd ed

  • : pbk

タイトル別名

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

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

: 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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詳細情報

  • NII書誌ID(NCID)
    BB19422777
  • ISBN
    • 9783319190440
    • 9783319369389
  • LCCN
    2015944813
  • 出版国コード
    xx
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    [S.l.],Cham
  • ページ数/冊数
    xiii, 349 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
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