From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes

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Ib H. Madsen (Aarhus Universitet, Denmark) Jxrgen Tornehave (Aarhus Universitet, Denmark)

From Calculus to Cohomology

De Rham Cohomology and Characteristic Classes

Ib H. Madsen (Aarhus Universitet, Denmark), Jxrgen Tornehave (Aarhus Universitet, Denmark)

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English

Cambridge University Press
12 May 1997

Mathematics & Sciences; Differential & Riemannian geometry; Algebraic topology

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.

By: Ib H. Madsen (Aarhus Universitet Denmark), Jxrgen Tornehave (Aarhus Universitet, Denmark)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 247mm, Width: 174mm, Spine: 19mm
Weight: 615g
ISBN: 9780521589567
ISBN 10: 0521589568
Pages: 296
Publication Date: 12 May 1997
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes

'... a self-contained exposition.' L'Enseignement 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