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Differential Topology : Graduate Texts in Mathematics, - Morris W. Hirsch

Differential Topology

Graduate Texts in Mathematics,

Hardcover Published: 16th September 1997
ISBN: 9780387901480
Number Of Pages: 222

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This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the back- ground material. In order to emphasize the geometrical and intuitive aspects of differen- tial topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors. In my view, advanced algebraic techniques like homology theory are better understood after one has seen several examples of how the raw material of geometry and analysis is distilled down to numerical invariants, such as those developed in this book: the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold, and so forth. With these as motivating examples, the use of homology and homotopy theory in topology should seem quite natural. There are hundreds of exercises, ranging in difficulty from the routine to the unsolved. While these provide examples and further developments of the theory, they are only rarely relied on in the proofs of theorems.

Industry Reviews

M.W. Hirsch

Differential Topology

"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology. Newly introduced concepts are usually well motivated, and often the historical development of an idea is described. There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text. "--MATHEMATICAL REVIEWS

Introduction
Manifolds and Maps
Function Spaces
Transversality
Vector Bundles and Tubular Neighborhoods
Degrees, Intersection Numbers and the Euler Characteristic
Morse Theory
Corbodism
Isotopy
Surfaces
Bibliography
Appendix
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387901480
ISBN-10: 0387901485
Series: Graduate Texts in Mathematics,
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 222
Published: 16th September 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.39 x 15.6  x 1.42
Weight (kg): 0.51
Edition Number: 6

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