ENGLISH

From calculus to cohomology: De Rham cohomology and characteristic classes

By Ib H. Madsen , Jxrgen Tornehave

Book information

Publisher
Cambridge University Press
Year
1997
ISBN
0521589568, 9780521589567
LCC
QA612.3 .M33 1997
Open Library ID
OL990253M
Language
english
Format
DJVU
Filesize
2 MB (2378815 bytes)
Pages
290\290
Topic
Mathematics Algebra
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2010-07-29 05:14:56

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, 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.

Similar books