Differential Topology by Morris Hirsch

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eBay item number:394185227550
Last updated on Nov 22, 2025 16:11:08 PSTView all revisionsView all revisions

Item specifics

Condition
Good: A book that has been read but is in good condition. Very minimal damage to the cover including ...
Publish Year
1997
Updated ISBN1
1468494511
Updated ISBN2
9781468494518
ISBN
9780387901480
Subject Area
Mathematics
Publication Name
Differential Topology
Publisher
Springer New York
Item Length
9.2 in
Subject
Topology
Publication Year
1976
Series
Graduate Texts in Mathematics Ser.
Type
Textbook
Format
Hardcover
Language
English
Author
Morris W. Hirsch
Features
Reprint
Item Weight
40.2 Oz
Item Width
6.1 in
Number of Pages
X, 222 Pages
Category

About this product

Product Identifiers

Publisher
Springer New York
ISBN-10
0387901485
ISBN-13
9780387901480
eBay Product ID (ePID)
144980

Product Key Features

Number of Pages
X, 222 Pages
Publication Name
Differential Topology
Language
English
Publication Year
1976
Subject
Topology
Features
Reprint
Type
Textbook
Author
Morris W. Hirsch
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover

Dimensions

Item Weight
40.2 Oz
Item Length
9.2 in
Item Width
6.1 in

Additional Product Features

Edition Number
5
Intended Audience
Scholarly & Professional
LCCN
97-205726
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, 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. "a?MATHEMATICAL 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, M.W. HirschDifferential 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
Dewey Edition
21
Series Volume Number
33
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
514/.72
Table Of Content
1 : Manifolds and Maps.- 0. Submanifolds of ?n+k.- 1. Differential Structures.- 2. Differentiable Maps and the Tangent Bundle.- 3. Embeddings and Immersions.- 4. Manifolds with Boundary.- 5. A Convention.- 2 : Function Spaces.- 1. The Weak and Strong Topologies on Cr(M, N).- 2. Approximations.- 3. Approximations on ?-Manifolds and Manifold Pairs.- 4. Jets and the Baire Property.- 5. Analytic Approximations.- 3 : Transversality.- 1. The Morse-Sard Theorem.- 2. Transversality.- 4 : Vector Bundles and Tubular Neighborhoods.- 1. Vector Bundles.- 2. Constructions with Vector Bundles.- 3. The Classification of Vector Bundles.- 4. Oriented Vector Bundles.- 5. Tubular Neighborhoods.- 6. Collars and Tubular Neighborhoods of Neat Submanifolds.- 7. Analytic Differential Structures.- 5 : Degrees, Intersection Numbers, and the Euler Characteristic.- 1. Degrees of Maps.- 2. Intersection Numbers and the Euler Characteristic.- 3. Historical Remarks.- 6 : Morse Theory.- 1. Morse Functions.- 2. Differential Equations and Regular Level Surfaces.- 3. Passing Critical Levels and Attaching Cells.- 4. CW-Complexes.- 7 : Cobordism.- 1. Cobordism and Transversality.- 2. The Thorn Homomorphism.- 8 : Isotopy.- 1. Extending Isotopies.- 2. Gluing Manifolds Together.- 3. Isotopies of Disks.- 9 : Surfaces.- 1. Models of Surfaces.- 2. Characterization of the Disk.- 3. The Classification of Compact Surfaces.
Edition Description
Reprint
Synopsis
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., 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.
LC Classification Number
QA613-613.8

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