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• catalog abstract "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 10 chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last 11 chapters cover Morse theory, index of vector fields, Poincare duality, vector bundles, connections and curvature, Chern and Euler classes, and Thom isomorphism, and the book ends with the general Gauss-Bonnet theorem. The text includes well 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.".
• catalog contributor b10292168.
• catalog contributor b10292169.
• catalog created "19976.".
• catalog date "1996".
• catalog date "19976.".
• catalog dateCopyrighted "19976.".
• catalog description "Ch. 1. Introduction -- Ch. 2. The Alternating Algebra -- Ch. 3. de Rham Cohomology -- Ch. 4. Chain Complexes and their Cohomology -- Ch. 5. The Mayer-Vietoris Sequence -- Ch. 6. Homotopy -- Ch. 7. Applications of de Rham Cohomology -- Ch. 8. Smooth Manifolds -- Ch. 9. Differential Forms on Smooth Manifolds -- Ch. 10. Integration on Manifolds -- Ch. 11. Degree, Linking Numbers and Index of Vector Fields -- Ch. 12. The Poincare-Hopf Theorem -- Ch. 13. Poincare Duality -- Ch. 14. The Complex Projective Space CP[superscript n] -- Ch. 15. Fiber Bundles and Vector Bundles -- Ch. 16. Operations on Vector Bundles and their Sections -- Ch. 17. Connections and Curvature -- Ch. 18. Characteristic Classes of Complex Vector Bundles.".
• catalog description "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 10 chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last 11 chapters cover Morse theory, index of vector fields, Poincare duality, vector bundles, connections and curvature, Chern and Euler classes, and Thom isomorphism, and the book ends with the general Gauss-Bonnet theorem.".
• catalog description "Includes bibliographical references and index.".
• catalog description "The text includes well 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.".
• catalog extent "vii, 286 p. :".
• catalog identifier "0521580595 (hc)".
• catalog identifier "0521589568 (pbk.)".
• catalog issued "1996".
• catalog issued "19976.".
• catalog language "eng".
• catalog publisher "New York : Cambridge University Press,".
• catalog subject "514/.2 20".
• catalog subject "Characteristic classes.".
• catalog subject "Differential forms.".
• catalog subject "Homology theory.".
• catalog subject "QA612.3 .M33 1997".
• catalog tableOfContents "Ch. 1. Introduction -- Ch. 2. The Alternating Algebra -- Ch. 3. de Rham Cohomology -- Ch. 4. Chain Complexes and their Cohomology -- Ch. 5. The Mayer-Vietoris Sequence -- Ch. 6. Homotopy -- Ch. 7. Applications of de Rham Cohomology -- Ch. 8. Smooth Manifolds -- Ch. 9. Differential Forms on Smooth Manifolds -- Ch. 10. Integration on Manifolds -- Ch. 11. Degree, Linking Numbers and Index of Vector Fields -- Ch. 12. The Poincare-Hopf Theorem -- Ch. 13. Poincare Duality -- Ch. 14. The Complex Projective Space CP[superscript n] -- Ch. 15. Fiber Bundles and Vector Bundles -- Ch. 16. Operations on Vector Bundles and their Sections -- Ch. 17. Connections and Curvature -- Ch. 18. Characteristic Classes of Complex Vector Bundles.".
• catalog title "From calculus to cohomology : de Rham cohomology and characteristic classes / Ib Madsen and Jørgen Tornehave.".
• catalog type "text".