- Paperback: 556 pages
- Publisher: Cambridge University Press; 1 edition (December 3, 2001)
- Language: English
- ISBN-10: 0521795400
- ISBN-13: 978-0521795401
- Product Dimensions: 7 x 1.4 x 10 inches
- Shipping Weight: 2.6 pounds (View shipping rates and policies)
- Average Customer Review: 3.9 out of 5 stars See all reviews (43 customer reviews)
- Amazon Best Sellers Rank: #319,451 in Books (See Top 100 in Books)
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Algebraic Topology 1st Edition
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"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
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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Top Customer Reviews
For beginners especially those who are serious about line-to-line rigorousness and clarity in definitions. This is not the book for you. To some extent, it may discourages you from the learning subject, especially if you are reading it on your own without a professor guiding you out of the labyrinth. For a beginner, the most important thing is to have a rigorous understanding of the basic definitions, the nuances in defintions and rigorous derivation upon these definitions. However, the geometrically intuitive flavor of hatcher's presentation should be reserved for "those experienced hikers who revisit the site at a second time" and who want to explore more places than their first visit. Hatcher does a good job for them, but for beginners, you shall just read the books, for instance, by Munkres which is much clearer than the murky conversation of Hatcher.
Unfortunately, this book is often recommended to beginners by those who are more experienced. To them, Hatcher's book of course gives a more matured discussion. But it is really overrated as an introductory text.
To be honest, this book, of course, deserves more than one star. But I hope to raise the awareness and let beginners have a better experience with algebraic topology without succumbing to the "peer pressure". It is ok to find this book confusing and frustrating if you are a beginner. It does not mean you are not good at it, or you are simply 'not smart' as those arrogant experienced guys. It just means this book is not a good introduction for beginners.
After learning the basics from the two Munkres book, THEN return to Hatcher.