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Algebraic Topology [Paperback]

Allen Hatcher
4.0 out of 5 stars  See all reviews (32 customer reviews)

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Book Description

December 3, 2001 0521535379 978-0521535373 1
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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Editorial Reviews

Review

"Algebraic topoligy books that emphasize geometrical intuition usually have only a modest technical reach. Remarkably, Hatcher (Cornell Univ.) offers a highly geometrical treatment that neverheless matches the coverage of, e.g., Edwin Henry Spanier's very formidable and identically titled classic work... He promises two advanced companion volumes, one on spectral sequences, one on vector bundles. One anticipates the combined treatise doing for algebraic topology what Michael Spivak's magisterial five-volume set did for differential geometry." Choice

Book 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. 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.

Product Details

  • Paperback: 556 pages
  • Publisher: Cambridge University Press; 1 edition (December 3, 2001)
  • Language: English
  • ISBN-10: 0521535379
  • ISBN-13: 978-0521535373
  • ASIN: 0521795400
  • Product Dimensions: 9.9 x 7 x 1.4 inches
  • Shipping Weight: 2.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (32 customer reviews)
  • Amazon Best Sellers Rank: #274,757 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
64 of 75 people found the following review helpful
5.0 out of 5 stars You would not regret if you buy this. February 26, 2003
By A Customer
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.
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21 of 22 people found the following review helpful
4.0 out of 5 stars The Good and the Bad May 25, 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. Read more ›
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50 of 61 people found the following review helpful
3.0 out of 5 stars Mixed Feelings February 4, 2007
Format:Paperback
This book is intended as an "introduction to alegbraic topology" and I rated the book accordingly.

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.
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67 of 83 people found the following review helpful
5.0 out of 5 stars The Last Text on Introductory Algebraic Topology January 4, 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.
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Most Recent Customer Reviews
5.0 out of 5 stars Best condition of this math book.
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 2 months ago by Rene Cabrera
5.0 out of 5 stars 5 stars for the motivation and examples
The more and more algebraic topology that I learn the more I continue to come back to Hatcher for motivation and examples. Read more
Published 9 months ago by louis.math
5.0 out of 5 stars Must Have
Hatcher's Algebraic Topology is a great introduction for this subject. The author introduces the concepts in a very clear and intuitive way, which helps a lot the reader. Read more
Published 12 months ago by E. Zanni
4.0 out of 5 stars Good introductory text
Hatcher seems to have become the standard text for algebraic topology. The book has great examples and many more illustrations than any other book I've seen on the subject. Read more
Published 12 months ago by Some guy
4.0 out of 5 stars Excellent Introduction to Algebraic Topology
This book is very clear, with a nice geometric flavor. Lots of pictures and examples to motivate the theory. Read more
Published 15 months ago by Isaac Solomon
3.0 out of 5 stars Improves once you get used to it
Over time, I have warmed a bit to Hatcher's book, especially after adapting to the style. Hatcher gives a comprehensive book which has been neatly organized into sections. Read more
Published 24 months ago by ece02006
1.0 out of 5 stars not a good book
This is not a good book in algebraic topology.
Not organized context, Not well-proved, Not even give you the direct definitions
Whatever it is, it is not Math book.
Published on May 24, 2012 by ramin
5.0 out of 5 stars All Time Favorite Math Textbook
This is a fantastic textbook, but don't take my word for it, you can download the entire book in pdf format from his website for free. Read more
Published on May 15, 2012 by Brian
5.0 out of 5 stars Great
This is one of the standard texts for this subject. It is a great introduction with a lot of classic problems.
Published on March 11, 2012 by uncountable
5.0 out of 5 stars What a lovely mathbook!
This is a wellknown classic, and a very very good mathbook, which I strongly recommend for reading. It is my favourite mathbook, no question about it. Read more
Published on October 26, 2011 by Pelle Salomonsson
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