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From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes

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From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes Cover

 

Synopses & Reviews

Publisher Comments:

De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters cover Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, Chern and Euler classes, Thom isomorphism, and the general Gauss-Bonnet theorem. The text includes over 150 exercises, and gives the background necessary for the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone who wishes to know about cohomology, curvature, and their applications.

Synopsis:

An introductory textbook on cohomology and curvature with emphasis on applications.

Synopsis:

De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The text includes well over 150 exercises, and gives the background to the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone studying cohomology, curvature, and their applications.

Synopsis:

An introductory textbook on cohomology and curvature with emphasis on applications.

Description:

Includes bibliographical references (p. 281) and index.

Table of Contents

1. Introduction; 2. The alternating algebra; 3. De Rham cohomology; 4. Chain complexes and their cohomology; 5. The Mayer-Vietoris sequence; 6. Homotopy; 7. Applications of De Rham cohomology; 8. Smooth manifolds; 9. Differential forms on smooth manifolds; 10. Integration on manifolds; 11. Degree, linking numbers and index of vector fields; 12. The Poincaré-Hopf theorem; 13. Poincaré duality; 14. The complex projective space CPn; 15. Fiber bundles and vector bundles; 16. Operations on vector bundles and their sections; 17. Connections and curvature; 18. Characteristic classes of complex vector bundles; 19. The Euler class; 20. Cohomology of projective and Grassmanian bundles; 21. Thom isomorphism and the general Gauss-Bonnet formula.

Product Details

ISBN:
9780521589567
Other:
Madsen, Ib
Author:
Tornehave, Jergen
Author:
Madsen, IB
Author:
Tornehave, Jxrgen
Author:
Madsen, Ib H.
Author:
Madsen/Tornehave
Publisher:
Cambridge University Press
Location:
Cambridge ;
Subject:
Applied
Subject:
Geometry - General
Subject:
Differential forms
Subject:
Topology
Subject:
Homology theory
Subject:
Characteristic classes.
Subject:
Topology - General
Subject:
MATHEMATICS / Topology
Edition Description:
Trade paper
Series Volume:
30
Publication Date:
19970131
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
296
Dimensions:
9.36x7.54x.64 in. 1.13 lbs.

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Related Subjects

History and Social Science » World History » General
Reference » Science Reference » Philosophy of Science
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes New Trade Paper
0 stars - 0 reviews
$63.25 In Stock
Product details 296 pages Cambridge University Press - English 9780521589567 Reviews:
"Synopsis" by , An introductory textbook on cohomology and curvature with emphasis on applications.
"Synopsis" by , De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The text includes well over 150 exercises, and gives the background to the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone studying cohomology, curvature, and their applications.
"Synopsis" by , An introductory textbook on cohomology and curvature with emphasis on applications.
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