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Algebraic Topology
 
 
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Algebraic Topology [Paperback]

Allen Hatcher (Author)
5.0 out of 5 stars  See all reviews (4 customer reviews)
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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

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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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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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5.0 out of 5 stars (4 customer reviews)
 
 
 
 
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5.0 out of 5 stars allen hatcher very nice book, Mar 11 2012
This review is from: Algebraic Topology (Paperback)
beatiful book on modern simplicial algebraic topology, nice examples and excellent methodology. basic constructions and more elaborated ones are exposed through several important examples
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2 of 3 people found the following review helpful
5.0 out of 5 stars You would not regret if you buy this., Feb 26 2003
By A Customer
This review is from: Algebraic Topology (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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2 of 3 people found the following review helpful
5.0 out of 5 stars The Last Text on Introductory Algebraic Topology, Jan 4 2002
By 
Pisheng Ding (New York, NY United States) - See all my reviews
This review is from: Algebraic Topology (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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