Topology
These notes discuss geometric and combinatorial topology and includes material on the classification of surfaces, embedding graphs on surfaces, map colouring and knot theory.
This latter topic includes material on the Alexander group of a knot, published here for the first time. This requires a basic knowledge of finitely presented abelian groups but a chapter is included to provide the relevant background knowledge for those who have never studied group theory.
[Please note that all links are to Adobe .pdf documents. They will open in a separate browser window.]
- Introduction and Contents
- CHAP01 Topological Spaces
- CHAP02 Surfaces
- CHAP03 Surgery on Surfaces
- CHAP04 Characterising Surfaces
- CHAP05 Graphs on Surfaces
- CHAP06 Graphs and Map Colouring
- CHAP07 Knots
- CHAP08 The Alexander Number
- CHAP09 Finitely Generated Abelian Groups
- CHAP10 The Alexander Group
- CHAP11 The Alexander Module
- CHAP12 Enumerating Knots
- CHAP13 Links