从微积分到上同调/天元基金影印系列丛书

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 form the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first 10 chapters study cohomolgy of open set 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 isoorphism,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 geomtry in four dimensions ,but it also serves as an introductory course in algebraic topology. It will be invaluable to any one who wishes to know abou cohomology,curvature,and their applications.