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About this book :-
A First Course in Algebraic Topology written by
Czes Kosniowski .
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.
Book Detail :-
Title: A First Course in Algebraic Topology
Edition:
Author(s): Czes Kosniowski
Publisher: Cambridge University Press
Series:
Year: 1980
Pages:
Type: PDF
Language: English
ISBN: 0521231957,9780521231954
Country:
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Book Contents :-
A First Course in Algebraic Topology written by
Czes Kosniowski
cover the following topics.
1. Sets and groups
2. Metric spaces, Topological spaces, Continuous functions
3. Induced topology, Quotient topology (and groups acting on spaces)
4. Product spaces, Compact spaces, Hausdorff spaces, Connected spaces
5. The pancake problems
6. Manifolds and surfaces
7. Paths and path connected spaces, The Jordan curve theorem
8. Homotopy of continuous mappings
9. 'Multiplication' of paths
10. The fundamental group, The fundamental group of a circle
11. Covering spaces, The fundamental group of a covering space, The fundamental group of an orbit space
12. The Borsuk-Ulam and ham-sandwhich theorems, More on covering spaces: lifting theorems, More on covering spaces: existence theorems
13. The SeifertVan Kampen theorem: I Generators; II Relations; III Calculations
14. The fundamental group of a surface
15. Knots: I Background and torus knots, Knots : II Tame knots, Table of Knots
16. Singular homology: an introduction
17. Suggestions for further reading
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