A First Course in Algebraic Topology
A First Course in Algebraic Topology
£44.99
GBPThis self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.
Product details
September 1980Paperback
9780521298643
280 pages
229 × 152 × 16 mm
0.41kg
Available
Table of Contents
- Preface
- Sets and groups
- 1. Background: metric spaces
- 2. Topological spaces
- 3. Continuous functions
- 4. Induced topology
- 5. Quotient topology (and groups acting on spaces)
- 6. Product spaces
- 7. Compact spaces
- 8. Hausdorff spaces
- 9. Connected spaces
- 10. The pancake problems
- 11. Manifolds and surfaces
- 12. Paths and path connected spaces
- 12A. The Jordan curve theorem
- 13. Homotopy of continuous mappings
- 14. 'Multiplication' of paths
- 15. The fundamental group
- 16. The fundamental group of a circle
- 17. Covering spaces
- 18. The fundamental group of a covering space
- 19. The fundamental group of an orbit space
- 20. The Borsuk-Ulam and ham-sandwhich theorems
- 21. More on covering spaces: lifting theorems
- 22. More on covering spaces: existence theorems
- 23. The Seifert_Van Kampen theorem: I Generators
- 24. The Seifert_Van Kampen theorem: II Relations
- 25. The Seifert_Van Kampen theorem: III Calculations
- 26. The fundamental group of a surface
- 27. Knots: I Background and torus knots
- 27. Knots : II Tame knots
- 28A. Table of Knots
- 29. Singular homology: an introduction
- 30. Suggestions for further reading
- Index.
