Description: From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes by IB Madsen 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher 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 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, Poincare 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. 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 Poincare-Hopf theorem; 13. Poincare 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. Review ... a self-contained exposition. LEnseignement Mathematique This is a very fine book. It treats de Rham cohomology in an intellectually rigourous yet accessible manner which makes it ideal for a beginning graduate student. Moreover, it gets beyond the minimal agenda that many authors have set ... A welcome addition. Mathematika ... a very polished completely self-contained introduction to the theory of differential forms ... the book is very well-written ... I recommend the book as an excellent first reading about curvature, cohomology and algebraic topology to anyone interested in these themes from students to active researchers, and especially to those who deliver lectures concerning the mentioned fields. Acta. Sci. Math. The book is written in a precise and clear language, it combines well topics from differential geometry, differential topology and global analysis. European Mathematical Society Promotional "Headline" An introductory textbook on cohomology and curvature with emphasis on applications. Description for Bookstore This text 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 studying cohomology, curvature, and their applications. Description for Library This text 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 studying cohomology, curvature, and their applications. Details ISBN0521589568 Author IB Madsen Short Title FROM CALCULUS TO COHOMOLOGY Pages 296 Publisher Cambridge University Press Language English ISBN-10 0521589568 ISBN-13 9780521589567 Media Book Format Paperback DEWEY 514.2 Illustrations Yes Year 1997 Publication Date 1997-03-31 Imprint Cambridge University Press Subtitle De Rham Cohomology and Characteristic Classes Place of Publication Cambridge Country of Publication United Kingdom Residence DK DOI 10.1604/9780521589567 Audience Professional and Scholarly UK Release Date 1997-03-13 AU Release Date 1997-03-13 NZ Release Date 1997-03-13 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:91375028;
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ISBN-13: 9780521589567
Book Title: From Calculus to Cohomology: de Rham Cohomology and Characteristi
Item Height: 238 mm
Item Width: 192 mm
Author: Ib H. Madsen, Jxrgen Tornehave
Publication Name: From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes
Format: Paperback
Language: English
Publisher: Cambridge University Press
Subject: Mathematics
Publication Year: 1997
Type: Textbook
Item Weight: 510 g
Number of Pages: 296 Pages