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A First Course in Algebraic Topology - Dr. Czes Kosniowski

A First Course in Algebraic Topology


Published: 24th November 1980
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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.

Sets and groups
Background: metric spaces
Topological spaces
Continuous functions
Induced topology
Quotient topology (and groups acting on spaces)
Product spaces
Compact spaces
Hausdorff spaces
Connected spaces
The pancake problems
Manifolds and surfaces
Paths and path connected spaces
The Jordan curve theorem
Homotopy of continuous mappings
'Multiplication' of paths
The fundamental group
The fundamental group of a circle
Covering spaces
The fundamental group of a covering space
The fundamental group of an orbit space
The Borsuk-Ulam and ham-sandwhich theorems
More on covering spaces: lifting theorems
More on covering spaces: existence theorems
The Seifert_Van Kampen theorem: I Generators
The Seifert_Van Kampen theorem: II Relations
The Seifert_Van Kampen theorem: III Calculations
The fundamental group of a surface
Knots: I Background and torus knots
Knots : II Tame knots
Table of Knots
Singular homology: an introduction
Suggestions for further reading
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521298643
ISBN-10: 0521298644
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 280
Published: 24th November 1980
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.6
Weight (kg): 0.41