Overview
Introduces the fundamental tools of differential topology
Ideally suited as a textbook for an orientation course for advanced-level research students or for independent study
Presents a number of epochal discoveries in the field of manifolds
Includes supplementary material: sn.pub/extras
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
Bibliographic Information
Book Title: Differential Topology
Authors: Amiya Mukherjee
DOI: https://doi.org/10.1007/978-3-319-19045-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Hindustan Book Agency 2015
Hardcover ISBN: 978-3-319-19044-0Published: 26 August 2015
Softcover ISBN: 978-3-319-36938-9Published: 29 October 2016
eBook ISBN: 978-3-319-19045-7Published: 30 June 2015
Edition Number: 2
Number of Pages: XIII, 349
Number of Illustrations: 25 b/w illustrations
Topics: Global Analysis and Analysis on Manifolds, Manifolds and Cell Complexes (incl. Diff.Topology)