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.
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本科低年級教材：每章中心命題放在首位作為目標，從歐式空間做黏貼推廣到可微流形；緊支集的意義就是將緊流形的結果推廣到非緊流形
评分4wrequired, ebook, only covered half
评分屎一樣的排版，讀瞭半年多放棄瞭。
评分其實這書如果循序漸進地讀來肯定是不錯的，不過當年為瞭一個期末作業連同調都不知道是啥的時候妄圖去看示性類，結果隻能是不懂，還連纍對此書的印象糟糕
评分其實這書如果循序漸進地讀來肯定是不錯的，不過當年為瞭一個期末作業連同調都不知道是啥的時候妄圖去看示性類，結果隻能是不懂，還連纍對此書的印象糟糕
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