Book:Donald W. Blackett/Elementary Topology: A Combinatorial and Algebraic Approach

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Donald W. Blackett: Elementary Topology: A Combinatorial and Algebraic Approach

Published $1982$, Academic Press.


Subject Matter


Contents

Preface
1. Some Examples of Surfaces
1.1 Coordinates on a Sphere and Torus
1.2 The Topological Sphere and Torus
1.3 Properties of the Sphere and Torus
1.4 The Cylinder and Möbius Band
1.5 Additional Representations of the Möbius Band
1.6 The Projective Plane
Exercises
2. The Classification of Surfaces
2.1 Surfaces and their Equations
2.2 Combinatorial Equivalence
2.3 The Canonical Equation
2.4 Combinatorial Invariants of a Surface
2.5 Topological Surfaces
Exercises
3. Complex Conics and Covering Surfaces
3.1 Complex Conics
3.2 Covering Surfaces
3.3 Some Additional Examples of Riemann Surfaces
Exercises
4. Mappings into the Sphere
4.1 Winding Number of a Plane Curve
4.2 Mappings into the Plane
4.3 The Brouwer Degree
4.4 Applications of the Winding Number in Complex Analysis
Exercises
5. Vector Fields
5.1 Vector Fields on the Plane
5.2 A Geographical Application
5.3 Vector Fields and Hydrodynamics
5.4 Vector Fields and Differential Equations
5.5 Vector Fields on a Sphere
5.6 Mappings of a Sphere onto Itself
Exercises
6. Network Topology
6.1 Introduction
6.2 Boundary and Coboundary
6.3 Paths, Circuits, and Trees
6.4 Basic Circuits
6.5 The Kirchhoff-Maxwell Laws
6.6 A Transportation Problem
Exercises
7. Some Three-Dimensional Topology
7.1 Three-Dimensional Manifolds
7.2 Orientability
7.3 Manifolds of Configurations
7.4 Topological Products and Fiber Bundles
Exercises


Bibliography
Subject Index