Algebraic Topology: An Intuitive Approach

✍ Scribed by Hajime Satō (author), Kiki Hudson (translator)

• Publisher: American Mathematical Society
• Year: 1999
• Tongue: English
• Leaves: 141
• Series: Translations of Mathematical Monographs, 183
• Edition: 1
• Category: Library

✦ Synopsis

The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references.Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Mobius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.

✦ Table of Contents

Cover
Title page
Contents
Preface
Preface to the English translation
Objectives
Homeomorphisms and homotopy equivalences
Topological spaces and cell complexes
Homotopy
Homology
Homology groups of cell complexes
Cohomology
The Universal coefficient theorem
Fiber bundles and vector bundles
Spectral sequences
A view from current mathematics
Appendix
Answers to exercises
Recommended Reading
Index
Back Cover

✦ Subjects

Algebraic Topology