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Title: Algebraic Topology
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Manufacturer: Cambridge University Press
List Price: $36.99
Our Price: $15.99
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| Customer Reviews: |
| Algebraic Topology by Cambridge University Press 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it from amazon though, it's available for free from Hatcher's website along with chapters of Spectral Sequences book (unpublished as of today).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. | | Algebraic Topology by Cambridge University Press 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 clear which definition is being used. I often had to search through several books to find a definition which seemed appropriate in the context of this text.
2. Useless or non-existant examples: When a definition is given, it is rarely followed by an example which illustrates it. When examples are present, they don't clearly illustrate the definition. It would be much better to have one well-written example for each definition (or at least for many definitions) rather than five examples for the same definition, none of which illustrates what each part of the definition is.
3. "It is clear": This phrase is used to such unreasonable extremes in this book that it makes me wonder why the book was written at all. If everything is so obvious, then why did you need to write a book about it? Algebraic topology is an inherently abstract and difficult subject, and the author should not have assumed that everything would be so obvious to all parties reading his text.
This book does have another redeeming quality: lots of exercises. Once you finally do understand the subject matter (whether due to a good instructor or a better reference textbook), there are lots of exercises to put your understanding to use. | | Algebraic Topology by Cambridge University Press 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 the theory but don't show the reader how to do much with it. In contrast, Hatcher spends a lot of time, appropriately, on some of first really important examples in topology, such as surfaces and projective spaces. These investigations are continued in the exercises, which I feel are the best thing about this book. Many of them contain juicy examples which really show how the geometry and algebra interact.
On the minus side, I would agree with another reviewer that sometimes the rambling style, which works quite well in the introduction to a new concept, sometimes gets in the way when it's time to get down to precise definitions and theorems. | | Algebraic Topology by Cambridge University Press 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 preliminary or complementary reading. Be warned that the styles are very different. Hatcher as well as Munkres like introducing the Fundamental Group pretty much right off the bat, which I like. However, there is something to be said to getting to beef up your geometric intuition by thinking about projective space and learning some classification theorems about compact manifolds and this is the approach of Massey. Massey is also nicer if you have just finished a first undergraduate course in topology.
Hatcher is definitely every algebraic topologist's bible and this really is just volume one in a whole series (check Hatcher's Cornell website for more info) of books that will be as monumental as Spivak's 5-volume Comprehensive Introduction to Differential Geometry (Which you should also buy as each volume is only ~$40). We should take a moment to pause and appreciate what Allen Hatcher has done by putting the book online for free. This is a tremendous statement that learning and knowledge should be free and accessible to anyone who seeks it. I know I first printed Chapter 0 out and starting reading it for free, but to be honest the quality of printing and binding done by the Cambridge University Press is worth the 30 bucks and you should pay it to keep academics warm and off the streets. | | Algebraic Topology by Cambridge University Press 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. | | Algebraic Topology by Cambridge University Press Product Description | | 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. |
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