作者：约翰·M.李（John
页数：433
出版社：世界图书出版公司
出版日期：2020
ISBN：9787519276089
电子书格式：pdf/epub/txt
内容简介
本书作者是美国华盛顿大学教授，具有丰富的教学经验, 他在华盛顿大学和哈佛大学教授流形课程已有15年之久。书中论述了流形理论中所需的拓扑学基本概念，特别是微分几何、代数几何和相关领域。线和曲面；同伦和基本群论；圆和球；群论；Seifert-Van Kampen定理；覆盖空间；覆盖类别；同调。
读者对象：数学、理论物理专业的高年级本科生、研究生以及相关的科研人员。
本书特色
拓扑流形是数学的一个很重要的分支，每个学习数学的同学和老师都值得拥有这样一部经典教材。
目录
Preface
1 Introduction
What Are Manifolds
Why Study Manifolds
2 Topological Spaces
Topologies
Convergence and Continuity
Hausdorff Spaces
Bases and Countability
Manifolds
Problems
3 New Spaces from Old
Subspaces
Product Spaces
Disjoint Union Spaces
Quotient Spaces
Adjunction Spaces
Topological Groups and Group Actions
Problems
4 Connectedness and Compactness
Connectedness
Compactness
Local Compactness
Paracompactness
Proper Maps
Problems
5 Cell Complexes
Cell Complexes and CW Complexes
Topological Properties of Cw Complexes
Classification of 1-Dimensional Manifold
Simplicial Complexes
Problems
6 Compact Surfaces
Surfaces
Connected Sums of Surfaces
Polygonal Presentations of Surfaces
The Classification Theorem
The Euler Characteristic
Orientability
Problems
7 Homotopy and the Fundamental Group
Homotopy
The Fundamental Group
Homomorphisms Induced by Continuous Maps
Homotopy Equivalence
Higher Homotopy Groups
Categories and Functors
Problems
8 The Circle
Lifting Properties of the Circle
1 Introduction
What Are Manifolds
Why Study Manifolds
2 Topological Spaces
Topologies
Convergence and Continuity
Hausdorff Spaces
Bases and Countability
Manifolds
Problems
3 New Spaces from Old
Subspaces
Product Spaces
Disjoint Union Spaces
Quotient Spaces
Adjunction Spaces
Topological Groups and Group Actions
Problems
4 Connectedness and Compactness
Connectedness
Compactness
Local Compactness
Paracompactness
Proper Maps
Problems
5 Cell Complexes
Cell Complexes and CW Complexes
Topological Properties of Cw Complexes
Classification of 1-Dimensional Manifold
Simplicial Complexes
Problems
6 Compact Surfaces
Surfaces
Connected Sums of Surfaces
Polygonal Presentations of Surfaces
The Classification Theorem
The Euler Characteristic
Orientability
Problems
7 Homotopy and the Fundamental Group
Homotopy
The Fundamental Group
Homomorphisms Induced by Continuous Maps
Homotopy Equivalence
Higher Homotopy Groups
Categories and Functors
Problems
8 The Circle
Lifting Properties of the Circle
