From Calculus to Cohomology pdf epub mobi txt 电子书下载 2024

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Ib H. Madsen

Cambridge University Press

1997-03-13

296

USD 39.99

Paperback

9780521589567

图书标签: 数学拓扑微分流形几何代数拓扑微分拓撲分析数学科学

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发表于2024-12-25

From Calculus to Cohomology epub 下载 mobi 下载 pdf 下载 txt 电子书下载 2024

From Calculus to Cohomology pdf epub mobi txt 电子书下载 2024

图书描述

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.

From Calculus to Cohomology 下载 mobi epub pdf txt 电子书