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

Subject Matter

 * Topology
 * Algebraic Topology

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