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' … this is a marvellous tome, which is indeed a delight to read. This book is destined to become very popular amongst students and teachers alike.' Bulletin of the Belgian Mathematical Society
'… clear and concise … makes the book useful both as a basis for courses and as a reference work.' Monatshefte für Mathematik
'… the truly unusual abundance of instructive examples and complementing exercises is absolutely unique of such a kind … the distinctly circumspect, methodologically inductive, intuitive, descriptively elucidating and very detailed style of writing give evidence to the fact that the author's first priorities are exactly what students need when working with such a textbook, namely clarity, readability, steady motivation, guided inspiration, increasing demand, and as much self-containedness of the exposition as possible. No doubt, a very devoted and experienced teacher has been at work here, very much so to the benefit of beginners in the field of algebraic topology, instructors, and interested readers in general.' Zentralblatt MATH
'… clear and concise … makes the book useful both as a basis for courses and as a reference work.' Monatshefte für Mathematik
'… the truly unusual abundance of instructive examples and complementing exercises is absolutely unique of such a kind … the distinctly circumspect, methodologically inductive, intuitive, descriptively elucidating and very detailed style of writing give evidence to the fact that the author's first priorities are exactly what students need when working with such a textbook, namely clarity, readability, steady motivation, guided inspiration, increasing demand, and as much self-containedness of the exposition as possible. No doubt, a very devoted and experienced teacher has been at work here, very much so to the benefit of beginners in the field of algebraic topology, instructors, and interested readers in general.' Zentralblatt MATH
Product Description
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. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: 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 a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book.
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The aim of this short preliminary chapter is to introduce a few of the most common geometric concepts and constructions in algebraic topology. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
The aim of this short preliminary chapter is to introduce a few of the most common geometric concepts and constructions in algebraic topology. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most Helpful Customer Reviews
0 of 3 people found the following review helpful
Format:Paperback
To find such an advanced text for so cheap is amazing. It will take me a while to get through it all though
Most Helpful Customer Reviews on Amazon.com (beta)
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27 reviews
59 of 70 people found the following review helpful
You would not regret if you buy this.
27 Feb 2003
Format:Paperback
There are many really good textbooks on algebraic topology and each has its own merit: Bredon for his effort in explaining everything that can be dealt without using spectral equences, Fomenko & Novikov for their effort in unifying differential geometry and algebraic/differential topology.
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.
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.
63 of 78 people found the following review helpful
The Last Text on Introductory Algebraic Topology
5 Jan 2002
Format:Paperback
No serious introductory text on basic algebraic topology has ever achieved this level of clarity, readability and depth. Its richness in examples (in both the main text and the problems) exposes a beginner to the underlying mechanisms of geometry in algebraic topology; its choice and arrangement of topics strike a perfect balance between accesibility and substantiveness; its lively and motivating exposition makes a student reluctant to attend the often boring topology classes. For a novice, this should be the first reading on the subject before (s)he is ruined by the many existing daunting texts; for a veteran, this can be very nourishing, especially if (s)he is already ruined by those either unreadable or shallow 'introduction's.
13 of 14 people found the following review helpful
The Good and the Bad
25 May 2006
Format:Paperback
Allen Hatcher has gone to great length's in order to create a text which, albeit overly verbose, can be used as a gentle introduction to modern Algebraic Topology. Why 'modern'? Compare this text with the tried and tested texts of Spanier, Munkres as well as May and, almost immediately, you will see what I mean. The obvious example is Hatcher's use of CW-complexes as opposed to the more traditional build up beginning with simplices. For the die-hard mathematician who enjoys less fluff, this book is not for you and, in particular, if this is your first venture in Algebriac Topology, you enjoy the theorem-proof-theorem style with a light sprinkling of explaination, then I would recommend J.J. Rotman's text. Whereas, if you enjoy filler, background information, and lots of side-notes or examples, then Hatcher's text would be a perfect fit. Myself, I fall into the category of those who enjoy the more terse texts but, I purchased Hatcher's (the hardcover) because of the clarity and percision found in the proofs. The majority of other texts have a tendancy to obfuscate the underlying meaning that should be unerstood by the up-and-coming mathematician. Of course this approach has it's merits since, in particular, it forces the reader to fill in the blanks but, as a matter of insight, Hatcher's approach is also beneficial. Another positive strength of Hatcher's text lies in the fact that he effectively breaks the subject into it's prime sub-categories in such a way that the reader can begin with either of the four parts of the text without having to rely too much on previous sections. This novel feature allows someone interested in, say, Cohomology to pick up an begin learning about Cohomology without having to waste time making their way through material they are not interested in. Finally, yes you can get the book for free via Hatcher's website but I highly recommend purchasing the hardback text. It is well made, it will last for years, and it becomes truely mobile as compared to burning your eyes out while reading the text on your computer. Moreover, why waste the time printing it out.
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