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Tables of Contents for Intuitive Combinatorial Topology
Chapter/Section Title
Page #
Page Count
Translator's Note
v
Introduction by the Editor of the Russian Original
vii
Introduction by the Authors
ix
Topology of Curves
1
30
The Concept of Continuity
1
3
What Is Topology Concerned With?
4
4
The Simplest Topological Invarients
8
3
The Euler Characteristic of a Graph
11
4
Intersection Index
15
4
The Jordan Curve Theorem
19
3
What Is a Curve?
22
6
Peano Curves
28
3
Topology of Surfaces
31
50
Euler's Theorem
31
2
Surfaces
33
5
The Euler Characteristic of a Surface
38
4
Classification of Closed Orientable Surfaces
42
6
Classification of Closed Nonorientable Surfaces
48
7
Vector Fields on Surfaces
55
5
The Four Color Problem
60
2
Coloring Maps on Surfaces
62
4
Wild Spheres
66
4
Knots
70
6
Linking Numbers
76
5
Homotopy and Homology
81
46
Periods of Multivalued Functions
81
2
The Fundamental Group
83
4
Cell Decompositions and Polyhedra
87
4
Coverings
91
4
The Degree of a Mapping and the Fundamental Theorem of Algebra
95
4
Knot Groups
99
5
Cycles and Homology
104
10
Topological Products
114
3
Fiber Bundles
117
4
Morse Theory
121
6
Appendix A: Topological Objects in Nematic Liquid Crystals
127
10
A.1. Nematics
128
1
A.2. Disclination in the Nematic
128
3
A.3. Disclination and Topology
131
3
A.4. Singular Points
134
2
A.5. What Else Is There?
136
1
Bibliography
137
2
Index
139