作者：M. A. Armstrong[著]
页数：12,251页
出版社：世界图书出版公司北京公司
出版日期：2008
ISBN：9787506283458
电子书格式：pdf/epub/txt
内容简介
本书特色一是注重培养学生的几何直观能力；二是对于单纯同调的处理重点比较突出，使主要线索不至于被复杂的细节所掩盖；三是注重抽象理论与具体应用的保持平衡。
作者简介
M.A.Armstrong，英国杜伦大学（Durham University）数学系教授。
目录
Preface
Chapter 1 Introduction
1.Euler’s theorem
2.Topological equivalence
3.Surfaces
4.Abstract spaces
5.A classification theorem
6.Topological invariants
Chapter 2 Continuity
1.Open and closed sets
2.Continuous functions
3.A space-filling curve
4.The Tietze extension theorem
Chapter 3 Compactness and connectedness
1.Closed bounded subsets of En
2.The Heine-Borel theorem
3.Properties of compact spaces
4.Product spaces
5.Connectedness
6.Joining points by paths
Chapter 4 Identification spaces
1.Constructing a Mobius strip
2.The identification topology
3.Topological groups
4.Orbit spaces
Chapter 5 The fundamental group
1.Homotopic maps
2.Construction of the fundamental group
3.Calculations
4.Homotopy type
5.The Brouwer fixed-point theorem
6.Separation of the plane
7.The boundary of a surface
Chapter 6 Triangulations
1.Triangulating spaces
2.Barycentric subdivision
3.Simplicial approximation
4.The edge group of a complex
5.Triangulating orbit spaces
6.Infinite complexes
Chapter 7 Surfaces
1.Classification
2.Triangulation and orientation
3.Euler characteristics
4.Surgery
5.Surface symbols
Chapter 8 Simplicial homology
1.Cycles and boundaries
2.Homology groups
3.Examples
4.Simplicial maps
5.Stellar subdivision
6.Invariance
Chapter 9 Degree and Lefschetz number
1.Maps of spheres
2.The Euler-Poincare formula
3.The Borsuk-Ulam theorem
4.The Lefschetz fixed-point theorem
5.Dimension
Chapter 10 Knots and covering spaces
1.Examples of knots
2.The knot group
3.Seifert surfaces
4.Covering spaces
5.The Alexander polynomial
Appendix: Generators and relations
Bibliography
Index
Chapter 1 Introduction
1.Euler’s theorem
2.Topological equivalence
3.Surfaces
4.Abstract spaces
5.A classification theorem
6.Topological invariants
Chapter 2 Continuity
1.Open and closed sets
2.Continuous functions
3.A space-filling curve
4.The Tietze extension theorem
Chapter 3 Compactness and connectedness
1.Closed bounded subsets of En
2.The Heine-Borel theorem
3.Properties of compact spaces
4.Product spaces
5.Connectedness
6.Joining points by paths
Chapter 4 Identification spaces
1.Constructing a Mobius strip
2.The identification topology
3.Topological groups
4.Orbit spaces
Chapter 5 The fundamental group
1.Homotopic maps
2.Construction of the fundamental group
3.Calculations
4.Homotopy type
5.The Brouwer fixed-point theorem
6.Separation of the plane
7.The boundary of a surface
Chapter 6 Triangulations
1.Triangulating spaces
2.Barycentric subdivision
3.Simplicial approximation
4.The edge group of a complex
5.Triangulating orbit spaces
6.Infinite complexes
Chapter 7 Surfaces
1.Classification
2.Triangulation and orientation
3.Euler characteristics
4.Surgery
5.Surface symbols
Chapter 8 Simplicial homology
1.Cycles and boundaries
2.Homology groups
3.Examples
4.Simplicial maps
5.Stellar subdivision
6.Invariance
Chapter 9 Degree and Lefschetz number
1.Maps of spheres
2.The Euler-Poincare formula
3.The Borsuk-Ulam theorem
4.The Lefschetz fixed-point theorem
5.Dimension
Chapter 10 Knots and covering spaces
1.Examples of knots
2.The knot group
3.Seifert surfaces
4.Covering spaces
5.The Alexander polynomial
Appendix: Generators and relations
Bibliography
Index
