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Algebraic Topology | 
 enlarge | Author: Allen Hatcher
Publisher: Cambridge University Press
Category: Book
List Price: $36.99
Buy New: $25.99
You Save: $11.00 (30%)
New (27) Used (20) from $16.00
Rating:  14 reviews
Sales Rank: 100193
Media: Paperback
Edition: 1
Pages: 550
Number Of Items: 1
Shipping Weight (lbs): 2.1
Dimensions (in): 9.9 x 6.8 x 1.6
ISBN: 0521795400
Dewey Decimal Number: 514.2
EAN: 9780521795401
Publication Date: November 15, 2001
Availability: Usually ships in 1-2 business days
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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.
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.
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| Customer Reviews: Read 9 more reviews...
 The Last Text on Introductory Algebraic Topology January 5, 2002
Pisheng Ding (New York, NY United States)
57 out of 67 found this review helpful
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.
You would not regret if you buy this. February 27, 2003
41 out of 45 found this review helpful
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.
Definitely a Bible August 22, 2007
Justin Curry
1 out of 2 found this review helpful
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.
Bible of Algebraic Topology May 8, 2007
C. Katouli (Huntington Beach, CA)
1 out of 3 found this review helpful
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.
Very good book, but don't buy it! February 19, 2005
Andrew Bruce (UK)
25 out of 36 found this review helpful
This book is avaliable free to download from Allen Hatcher's webpage. You will also find other books he has written.
http://www.math.cornell.edu/~hatcher/
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