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Differential topology

Mukherjee, Amiya.

Differential topology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Differential topologyby Amiya Mukherjee.
作者:	Mukherjee, Amiya.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xiii, 349 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Differential topology.
電子資源:	http://dx.doi.org/10.1007/978-3-319-19045-7
ISBN:	9783319190457 (electronic bk.)

Differential topology
Mukherjee, Amiya.

Differential topology[electronic resource] /by Amiya Mukherjee. - 2nd ed. - Cham :Springer International Publishing :2015. - xiii, 349 p. :ill., digital ;24 cm.

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. .

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.

ISBN: 9783319190457 (electronic bk.)

Standard No.: 10.1007/978-3-319-19045-7doiSubjects--Topical Terms:

212318
Differential topology.

LC Class. No.: QA613.6

Dewey Class. No.: 514.72

Differential topology
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505 0 $a 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. .
520 $a 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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