作者：MorrisW.Hirsch[著]
页数：10,221页
出版社：世界图书出版公司
出版日期：2019
ISBN：9787519255879
电子书格式：pdf/epub/txt
内容简介
微分拓扑学有三个主要的研究领域：纤维丛、复流形和微分流形。本书对应用于微分流形和微分映射研究的拓扑学，对其基本思想作了全面的介绍，书中体现了作者的独特简明风格和独立的观点。取材得当，结构清晰，例题精彩，习题丰富，并尽量不使用代数拓扑的方法而是把几何分析内容提炼成一些数值不变量入手。
目次：①流域和映射，②函数空间，③横割性，④向量丛和管状邻。⑤映射度、相交数和欧拉示性数，⑥Morse理论，⑦协边理论，⑧合痕，⑨曲面。
读者对象：数学及相关专业的研究生。
作者简介
《微分拓扑学》作者M.W.Hirsch（M.W.赫希）是美国加利福尼亚大学（University Of California）数学系教授，曾出版多部著作。
本书特色
微分拓扑学有三个主要的研究领域：纤维丛、复流形和微分流形。本书对应用于微分流形和微分映射研究的拓扑学，对其基本思想作了全面的介绍，书中体现了作者的独特简明风格和独立的观点。取材得当，结构清晰，例题精彩，习题丰富，并尽量不使用代数拓扑的方法而是把几何分析内容提炼成一些数值不变量入手。
目次：①流域和映射，②函数空间，③横割性，④向量丛和管状邻。⑤映射度、相交数和欧拉示性数，⑥Morse理论，⑦协边理论，⑧合痕，⑨曲面。
读者对象：数学及相关专业的研究生。
目录
Introduction
Chapter 1 Manifolds and Maps
0.Submanifolds of Rn+k
1.Differential Structures
2.Differentiable Maps and the Tangent Bundle
3.Embeddings and Immersions
4.Manifolds with Boundary
5.A Convention
Chapter 2 Function Spaces
1.The Weak and Strong Topologies on C'(M,N)
2.Approximations
3.Approximations on 0-Manifolds and Manifold Pairs
4.Jets and the Baire Property
5.Analytic Approximations
Chapter 3 Transversality
1.The Morse-Sard Theorem
2.Transversality
Chapter 4 Vector Bundles and Tubular Neighborhoods
1.Vector Bundles
2.Constructions with Vector Bundles
3.The Classification of Vector Bundles
4.Oriented Vector Bundles
5.Tubular Neighborhoods
6.Collars and Tubular Neighborhoods of Neat Submanifolds
7.Analytic Differential Structures
Chapter 5 Degrees, Intersection Numbers,and the Euler Characteristic
1.Degrees of Maps
2.Intersection Numbers and the Euler Characteristic
3.Historical Remarks
Chapter 6 Morse Theory
1.Morse Functions
2.Differential Equations and Regular Level Surfaces
3.Passing Critical Levels and Attaching Cells
4.C W-Complexes
Chapter 7 Cobordism
1.Cobordism and Transversality
2.The Thorn Homomorphism
Chapter 8 Isotopy
1.Extending Isotopies
2.Gluing Manifolds Together
3.Isotopies of Disks
Chapter 9 Surfaces
1.Models of Surfaces
2.Characterization of the Disk
3.The Classification of Compact Surfaces
Bibliooraphy
Appendix
Index
Chapter 1 Manifolds and Maps
0.Submanifolds of Rn+k
1.Differential Structures
2.Differentiable Maps and the Tangent Bundle
3.Embeddings and Immersions
4.Manifolds with Boundary
5.A Convention
Chapter 2 Function Spaces
1.The Weak and Strong Topologies on C'(M,N)
2.Approximations
3.Approximations on 0-Manifolds and Manifold Pairs
4.Jets and the Baire Property
5.Analytic Approximations
Chapter 3 Transversality
1.The Morse-Sard Theorem
2.Transversality
Chapter 4 Vector Bundles and Tubular Neighborhoods
1.Vector Bundles
2.Constructions with Vector Bundles
3.The Classification of Vector Bundles
4.Oriented Vector Bundles
5.Tubular Neighborhoods
6.Collars and Tubular Neighborhoods of Neat Submanifolds
7.Analytic Differential Structures
Chapter 5 Degrees, Intersection Numbers,and the Euler Characteristic
1.Degrees of Maps
2.Intersection Numbers and the Euler Characteristic
3.Historical Remarks
Chapter 6 Morse Theory
1.Morse Functions
2.Differential Equations and Regular Level Surfaces
3.Passing Critical Levels and Attaching Cells
4.C W-Complexes
Chapter 7 Cobordism
1.Cobordism and Transversality
2.The Thorn Homomorphism
Chapter 8 Isotopy
1.Extending Isotopies
2.Gluing Manifolds Together
3.Isotopies of Disks
Chapter 9 Surfaces
1.Models of Surfaces
2.Characterization of the Disk
3.The Classification of Compact Surfaces
Bibliooraphy
Appendix
Index
