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Algebraic Topology
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Binding: Paperback
Dewey Decimal Number: 514.2
EAN: 9780521795401
Edition: 1
ISBN: 0521795400
Label: Cambridge University Press
Manufacturer: Cambridge University Press
Number Of Items: 1
Number Of Pages: 550
Publication Date: November 15, 2001
Publisher: Cambridge University Press
Studio: Cambridge University Press
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Editorial Review:
In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. A unique feature of the book is the inclusion of many optional topics for which elementary expositions are hard to find. Researchers and students alike will welcome this aspect of the book.
Customer Reviews
Average Rating: 
Rating:  - very good!
I like this book a lot! It's comprehensive and clear and has lots of examples. Don't buy it from amazon though, it's available for free from Hatcher's website along with chapters of Spectral Sequences book (unpublished as of today). My only criticism is that the book is a bit dry, the common problem with algebraic topology texts.
Rating:  - One of the worst textbooks ever.
The only good thing about this textbook is that it contains possibly every topic that an instructor could conceive of covering in an introductory course in algebraic topology. However, there are several flaws which prevented me from getting much out of this book:
1. Lack of definitions: I agree with another reviewer of this text who stated that this book does not give definitions. It often does not define objects which not only have several equivalent definitions, but it is not even ... Read More
Rating: - Excellent book for geometers
I have taught graduate algebraic topology courses three times from this book. My overall feeling is that, despite a few flaws, I have not seen another book I would rather use -- and I really wish this book had been around when I was learning the subject! I appreciate its very geometric style and the way it tries to get the reader to "see" the definitions of homology, homotopy, etc, before diving into the rigorous treatment. Many algebraic topology books I have seen are nearly example-free; they build ... Read More
Rating: - Definitely a Bible
This is certainly a modern classic that predominates algebraic topology courses like 18.905/6 at MIT and Part II and III Mathematical Tripos at Cambridge. It is also perfectly suited to personal study and reading -- savor it and its geometric beauty! I would warn the absolute beginner that the text may seem steep at first (especially if you start with Chapter 0 first, the beginning of Chapter 1 is easier) and slightly unmotivated. I would recommend Massey's "Algebraic Topology: An introduction" GTM 56 for ... Read More
Rating: - Bible of Algebraic Topology
You can not find a better book that explains and covers this beautiful subject better than Allen Hatcher's Algebraic Topology. The subject is build up very well and there are tons of examples that will help you deepen your understanding. I read this book in parallel with Sato (Algebraic Topology: An Intuitive Approach) and Munkres (Topology, 2nd Edition) for independent study. This combination is working well for me, but don't expect to get the same results as you would if you had a great teacher.
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