Surface topology

This updated and revised edition of a widely acclaimed and successful text for undergraduates examines topology of recent compact surfaces through the development of simple ideas in plane geometry. Containing over 171 diagrams, the approach allows for a straightforward treatment of its subject area. It is particularly attractive for its wealth of applications and variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry.Examines topology of recent compact su.

Front Cover; About Our Authors; Surface Topology; Copyright Page; Table of Contents; Notation; Authors' preface; Preface to this 3rd edition; Chapter 1. Intuitive ideas; 1.1 INTRODUCTION; 1.2 PRELIMINARY SKIRMISH; 1.3 MODELS; 1.4 CONNECTED SETS; 1.5 PROBLEM SURFACES; 1.6 HOMEOMORPHIC SURFACES; 1.7 SOME BASIC SURFACES; 1.8 ORIENTABILITY; 1.9 THE CONNECTED SUM CONSTRUCTION; 1.10 SUMMARY; 1.11 EXERCISES; Chapter 2. Plane models of surfaces; 2.1 THE BASIC PLANE MODELS; 2.2 PAPER MODELS OF THE BASIC SURFACES; 2.3 PLANE MODELS AND ORIENTABILITY; 2.4 CONNECTED SUMS OF THE BASIC SURFACES; 2.5 SUMMARY

5.3 REGULAR COMPLEXES5.4 b-VALENT COMPLEXES; 5.5 COMMENTS; 5.6 EXERCISES; Chapter 6. Maps and graphs; 6.1 COLOURING MAPS ON SURFACES; 6.2 EMBEDDING GRAPHS IN SURFACES; 6.3 PLANAR GRAPHS; 6.4 OUTERPLANAR GRAPHS; 6.5 EMBEDDING THE COMPLETE GRAPHS; 6.6 SPROUTS; 6.7 BRUSSELS SPROUTS; 6.8 COMMENTS; 6.9 EXERCISES; Chapter 7. Vector fields on surfaces; 7.1 A WATER PROOF; 7.2 HAIRY SURFACES; 7.3 INTERPRETATIONS OF THE INDEX THEOREM; 7.4 LAKES; 7.5 ISLANDS IN LAKES; 7.6 ISLANDS; 7.7 VECTOR FIELDS AND DIFFERENTIAL EQUATIONS; 7.8 COMMENTS; 7.9 EXERCISES

Chapter 8. Plane tessellation representations of…