Explorations in Topology

Explorations in Topology: Map Coloring, Surfaces and Knots 是 David A. Gay 写的一本关于低维拓扑学(Low-dimensional topology)(map coloring, surfaces, and knots)的书. 第一版是 2007 年出现的, 现在 Elsevier Inc. 推出的新版对学生和研究者都是有价值的.

本书侧重解决问题(problem-solving), 自然的展现了概念的发展.

本书分为十四章. 第四章论述如何采用四种颜色来给地图染色, 第十二章则讲解如何给曲面上的地图进行染色.

Color a Map with Four Colors

Table of Contents

Front-matter, Pages i,iii
Copyright, Page iv
Dedication, Page v
Preface, Pages xi-xiii
Acknowledgments, Page xv
1 Acme Does Maps and Considers Coloring Them, Pages 1-25
2 Tours, Pages 27-46
3 Maps Data, Pages 47-68
4 Map Data and Map Coloring, Pages 69-82
5 How to Color a Map with Four Colors, Pages 83-97
6 Doughnuts, Pages 99-120
7 The Möbius Strip, Pages 121-142
8 New Worlds: Klein Bottles and Other Surfaces, Pages 143-168
9 Surface Sums and Euler Numbers, Pages 169-192
10 Classification of Surfaces, Pages 193-209
11 Classification (Part II), Existence and Four-Space, Pages 211-238
12 Coloring Maps on Surfaces, Pages 239-256
13 Knots, Pages 257-295
14 Projects, Pages 297-315

Author: David A. Gay
ISBN: 978-0-12-416648-6
2014 Elsevier Inc.