Differential Topology

Amiya Mukherjee

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English

Birkhauser Verlag AG
29 October 2016

Numerical analysis; Analytic geometry; 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.

By: Amiya Mukherjee
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 2nd ed. 2015
Dimensions: Height: 235mm, Width: 155mm, Spine: 19mm
Weight: 5.504kg
ISBN: 9783319369389
ISBN 10: 3319369385
Pages: 349
Publication Date: 29 October 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Reviews for Differential Topology

“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)