- 作 者：Sue E. Goodman
- 出 版 社：American Mathematical Society
- 出版年份：2009
- ISBN：0821847961
- 标注页数：236 页
- PDF页数：253 页
请阅读订购服务说明与试读!
订购服务说明
1、本站所有的书默认都是PDF格式，该格式图书只能阅读和打印，不能再次编辑。
2、除分上下册或者多册的情况下，一般PDF页数一定要大于标注页数才建议下单购买。【本资源253 ≥236页】
图书下载及付费说明
1、所有的电子图书为PDF格式，支持电脑、手机、平板等各类电子设备阅读；可以任意拷贝文件到不同的阅读设备里进行阅读。
2、电子图书在提交订单后一般半小时内处理完成,最晚48小时内处理完成。(非工作日购买会延迟)
3、所有的电子图书都是原书直接扫描方式制作而成。
1INTRODUCTION TO POINT SET TOPOLOGY 1
1.1 Open and Closed Sets 1
1.2 Continuous Functions 12
1.3 Some Topological Properties 22
1.4 A Brief Introduction to Dimension（Optional） 31
2SURFACES 36
2.1 Definition of a Surface 36
2.2 Connected Sum Construction 39
2.3 Plane Models of Surfaces 41
2.4 Orientability 54
2.5 Plane Models of Nonorientable Surfaces 56
2.6 Classification of Surfaces 57
2.7 Proof of the Classification Theorem for Surfaces（Optional） 59
3THE EULER CHARACTERISTIC 66
3.1 Cell Complexes and the Euler Characteristic 67
3.2 Triangulations 75
3.3 Genus 77
3.4 Regular Complexes 80
3.5 b-Valent Complexes 86
4MAPS AND GRAPHS 90
4.1 Maps and Map Coloring 91
4.2 The Five-Color Theorem for S2 98
4.3 Introduction to Graphs 101
4.4 Graphs in Surfaces 107
4.5 Embedding the Complete Graphs and Graph Coloring 113
5VECTOR FIELDS ON SURFACES 118
5.1 Vector Fields in the Plane 119
5.2 Index of a Critical Point 122
5.3 Limit Sets in the Plane 131
5.4 A Local Description of a Critical Point 133
5.5 Vector Fields on Surfaces 141
6THE FUNDAMENTAL GROUP 152
6.1 Path Homotopy and the Fundamental Group 153
6.2 The Fundamental Group of the Circle 160
6.3 Deformation Retracts 164
6.4 Further Calculations 167
6.5 Presentations of Groups 171
6.6 Seifert-van Kampen Theorem and the Fundamental Groups of Surfaces 173
6.7 Proof of the Seifert-van Kampen Theorem 179
7INTRODUCTION TO KNOTS 182
7.1 Knots：What They Are and How to Draw Them 183
7.2 Prime Knots 190
7.3 Alternating Knots 191
7.4 Reidemeister Moves 193
7.5 Some Simple Knot Invariants 194
7.6 Surfaces with Boundary 202
7.7 Knots and Surfaces 207
7.8 Knot Polynomials 219
Bibliography and Reading List 230
Index 234