Book:Donald W. Blackett/Elementary Topology/Second Edition

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Donald W. Blackett: Elementary Topology: A Combinatorial and Algebraic Approach (2nd Edition)

Published $\text {1982}$, Academic Press.

Subject Matter


Preface to the Revised Editionm
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
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
3. Complex Conics and Covering Surfaces
3.1 Complex Conics
3.2 Covering Surfaces
3.3 Some Additional Examples of Riemann Surfaces
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
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
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
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

Subject Index

Further Editions