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Algebraic Topology 1st Edition
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Top Customer Reviews
Hatcher's book is intended as one of the series that cover every aspect of the subject. Separate books on vector bundles and K-theory, and spectral sequences respectively, are to appear sometime in the future. Thus this one covers ordinary homology/cohomology and homotopy theory only. His writing style is helpful and user-friendly, not demanding extensive "mathematical maturity".
I am not sure if this is "the" textbook on algebraic topology, but I bet this is among the best ones. You would not regret if you buy this, even when an electronic version is available online (for free) from the author's home page.
I found the book refreshing at points and thorougly frustrating at other points. This was one of the first book I approached when trying to learn formal algebraic topology. Prior to reading it I had indirect exposure to algebraic topology in application to physics especially when learning about differential forms where one is usually exposed to homology cohomology and derham cohomology, etc. I found the physics texts MUCH more instructive than this text which is supposed to be from the mathematicians perspective.
The book has it's merits:
1) it is organized well and attempts to relate the main topics in algebraic topolgy - homotopy and homology
2) it has many examples to help solidify the concept presented
3) it has plenty of exercises of varying difficulty.
4) it genuinely tries to motivate the mathematical ideas of algebraic topology.
However it has many faults. I was particulary disturbed by it's lack of definitions. At some point I felt like I was having a conversation or reading a "pop" math books for the dilettante not mathematician. I found myself repeatedly going back and having to REREAD THE TEXT to get the definition of some mathematical object. In my humble opinion a math text should clearly state definitions and properties and not try to "explain" them in prose without the preceding definitions.
The author also states minimal prerequisites ( algebra and point set topology ), however, it is clear alot more is needed.
Although there are plenty of examples, the author, simply states conclusions which maybe "self-evident" to someone with previous exposure to algebraic topology but not to a novice.Read more ›
Most Recent Customer Reviews
This book is amazing. Its also free from their website, but having a paper copy I find is much better for studyingPublished 7 months ago by Amazon Customer
As many others have explained, this book has an informal style in defining new concepts and its proofs. Read morePublished 11 months ago by Unknown
Bought this as a textbook for a class. Great as a reference but the proofs are too dense to follow easily; would not suggest for learning algebraic topology for the first time.Published 17 months ago by Sara T
Rigorous text with abundant diagrams, examples, and motivation. This is as good as mathematical writing gets.Published 18 months ago by Tom Ashmore
I agree with most of the reviews on this page. Hatcher's Algebraic Topology is a great introduction to the subject, and it has superb explanations of the geometrical notions that... Read morePublished 22 months ago by Dan Irvine
I use this book to teach Algebraic Topology. I like this book: informal ideas of the new constructions and motivation are explained first and then rigorous definitions and proofs. Read morePublished 23 months ago by Victor Turchin
This book was in the best newest condition ever. For a paper bag it was complete, well treated, and clean. Very satisfied with this purchase!Published on May 7, 2014 by Rene Cabrera