A First Course in Algebraic Topology

This self-contained introduction to algebraic topology is suitable for a number of topology courses.

Czes Kosniowski (Author)

9780521298643, Cambridge University Press

Paperback, published 25 September 1980

280 pages
22.9 x 15.2 x 1.6 cm, 0.41 kg

This 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.

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.

Subject Areas: Mathematics [PB]