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Elements Of Algebraic Topology, by James R. Munkres
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Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature�of�algebraic topology�for�beginners.
- Sales Rank: #737551 in Books
- Published on: 1996-01-01
- Ingredients: Example Ingredients
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x 1.06" w x 6.00" l, 1.53 pounds
- Binding: Paperback
- 464 pages
Most helpful customer reviews
37 of 40 people found the following review helpful.
Excellent text on homology and cohomology
By Kevin M. Iga
Algebraic topology is a tough subject to teach, and this book does a very good job. Some prerequisites, however, are essential:
* point set topology (e.g. in Munkres' Topology)
* Abstract algebra
* Mathematical maturity to be willing to follow a definition and argument even when it seems like a weird side-track
In addition, this would not be the first book I would recommend to those interested in algebraic topology. First might be Massey's "Algebraic Topology: and Introduction" that introduces the fundamental group (conceptually easier than homology and cohomology).
At some point, however, a prospective student in topology will have to learn homological algebra and this provides the most concrete approach I know to the subject.
Algebraic topology is a lot of fun, but many of the previous textbooks had not given that impression. This one does.
21 of 24 people found the following review helpful.
A little incomplete
By Bernardo Vargas
This well written text is one of the standard references in algebraic topology courses because of its conciseness, and I find it very useful as a reference text.
However I think it is a little incomplete because of several reasons.
(1)It pays no attention to one basic concept of algebraic topology: the fundamental group.
(2) It doesn't cover ^Cech homology, important in other areas, like dimension theory for example.
(3) It doesn't stress the most important feature of algebraic topology: its connection to other areas of mathematics (analysis, differential geometry, etc.).
(4) Its list of references is too short, and lacks almost completely HISTORICAL references which are always important to become an expert in any field.
Conclusion: a good reference on homology and cohomology essentials, but not "the" reference on algebraic topology as a whole.
12 of 15 people found the following review helpful.
The book binding is horrible
By A Customer
The material in the book (homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, applications to classical theorems of point-set topology) is for the most part solid. However...
- Munkres really belabors the simplicial theory, and it gets to be quite painful (especially the *CHAPTER* on the topological invariance of simplicial homology groups).
- Some very important topics (homotopy theory, fiber bundles) are not at all discussed.
- The book binding is horrible -- my copy is in two pieces, with several loose pages, and I don't think the hardcover edition is still in print.
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