Graphs, Surfaces and Homology
Graphs, Surfaces and Homology
Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.
- At last, this book is back in print, with updated references and redesigned illustrations
- Numerous examples introduce the main theorems of homology theory, enabling the reader to understand basic concepts and gradually develop their understanding
- No prerequisites beyond elementary algebra
Product details
August 2010Paperback
9780521154055
272 pages
227 × 151 × 15 mm
0.39kg
150 b/w illus. 200 exercises
Available
Table of Contents
- Preface to the third edition
- Preface to the first edition
- List of notation
- Introduction
- 1. Graphs
- 2. Closed surfaces
- 3. Simplicial complexes
- 4. Homology groups
- 5. The question of invariance
- 6. Some general theorems
- 7. Two more general theorems
- 8. Homology modulo 2
- 9. Graphs in surfaces
- Appendix. Abelian groups
- References
- Index.
