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

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## Donald W. Blackett:

## 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**