Algebraic Topology: An Intuitive Approach

by Hajime Sato

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.

Genres: Mathematics

118 pages, Paperback

First published February 1, 1999

Reviews

[Woflmao · Rating 2 out of 5]

Never trust anyone who claims to teach you the intuition behind topology. Once you get past the first few pretty pictures of tori, knots or links magically unlinking themselves, either the lesson is over or the explanations degenerate into incomprehensible handwaving which, due to a lack of preciseness, is rarely comprehensible.
Sato's book on topology is no different. It starts out nicely explaining homotopy and homeomorphisms using letters and knots, does a reasonable job at showing quotient spaces and cell complexes, and once we get to homology, Sato reverts back to the axiomatic introduction because it is "neat and tidy". How intuitive is that? No recovery from that point on.
The book clearly does not deliver on its promise to be an intuitive introduction, but it also fails as a rigorous textbook because so many details are omitted. On top of that it is riddled with typos.

[Alileo · Rating 3 out of 5]

Konunun günümüz çalışmalarına hızlıca gelmek gibi bir amacı var belli ki ama bu kadar kompleks bir konuyu ısrarla "giriş seviyesinde" anlattığını iddia etmesi kötü olmuş. Yine iddia ettiği gibi sezgisel bir yaklaşım değil açıklamaları bence. Kendi iddiasının ötesinde, bir çeşit özetleme çabası olarak değerlendirilebilir.