GRAPHS, SURFACES, AND KNOTS

An Introduction

 

 

 

 

 

by

 

 

 

 

 

SAUL STAHL

DEPARTMENT OF MATHEMATICS

UNIVERSITY OF KANSAS

LAWRENCE, KS 66045

 

 

 

Copyright 2000

TABLE OF CONTENTS

 

 

 

1. Topological spaces and homeomorphisms

2. Graphs

2.1 Nodes and Arcs

2.2 Traversability

2.3 Colorings

2.4 Planarity

2.5 Graph homeomorphisms (optional)

3. Surfaces

3.1 Introduction

3.2 The Classification of Surfaces

3.3 Operations on Surfaces

3.4 Bordered Surfaces

3.5 Riemann Surfaces (optional)

4. Graphs on surfaces (optional)

4.1 Embeddings and Their Regions

4.2 Polygonal Embeddings

4.3 The Embeddings of a Graph

5. Knots and Links

5.1 Preliminaries

5.2 Labelings

5.3 From Graphs to Links and on to Surfaces

5.4 The Jones Polynomial

5.5 Alternating Diagrams

5.6 Knots and Surfaces

Index