From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes - Couverture souple

Madsen, Ib

 
9780521589567: From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes
Couverture souple
ISBN 10 : 0521589568 ISBN 13 : 9780521589567
Editeur : Cambridge University Press, 1997

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 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 include Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, and the book ends with the general Gauss-Bonnet theorem. 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Revue de presse

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

'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

Présentation de l'éditeur

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 include Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, and the book ends with the general Gauss-Bonnet theorem. 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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
1997
Langue
anglais
ISBN 10 
0521589568
ISBN 13 
9780521589567
Reliure
Broché
Nombre de pages
296
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

chemin des peupliers 27
Dardilly
France

Autres éditions populaires du même titre

9780521580595: From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes

Edition présentée

ISBN 10 :  0521580595 ISBN 13 :  9780521580595
Editeur : Cambridge University Press, 1997
Couverture rigide