天元基金影印系列丛书 从微积分到上同调 英文版
作者：（丹）马森（Madsen，I.H.），（丹）托内哈弗（Tornehave，J.） 著
出版时间：2003年版
丛编项： 天元基金影印系列丛书
内容简介
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.
目录
Preface
Chapter 1 Introduction
Chapter 2 The Alternating Algebra
Chapter 3 de Rham Cohomology
Chpater 4 Chain Complexes and their Cohomology
Chpater 5 The Mayer-Vietoris Sequence
Chpater 6 Homotopy
Chpater 7 Applications of de Rham Cohomology
Chpater 8 Smooth Manifolds
Chapter 9 Differential Forms on Smoth Manifolds
Chapter 10 Integration on Meanifolds
Chapter 11 Degree,Linking Numbers and Index of Vector Fields
Chapter 12 The Poincare-Hopf Theorem
Chapter 13 Poincare Duality
Chapter 14 The Complex Projective Space CPn
Chapter 15 Fiber Bundles and Vector Bundles
Chapter 16 Operations on Vector Bundles and their Sections
Chapter 17 Connections and Curvature
Chapter 18 Characteristic Classes of Complex Vector Bundles
Chapter 19 The Euler Class
Chapter 20 Cohomology of Projective and Grassmannian Bundles
Chapter 21 Thom Isomorphism and the General Gauss-Bonnet Formula
Appendix A Smooth Partition of Unity
Appendix B Invariant Polynomials
Appendix C Proof of Lemmas 12.12and 12.13
Appendix D Exericises
References
Index
