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while a person with enough prior knowledge will not get anything out of it either. (A trivial example I've noted is that articles write "topological equivalence" rather than homeomorphism. This is a disservice to everybody; the person that does not know any math will not get a better understanding, while say a student of math will wonder if this is a concept that he/she has not yet encountered, so will be forced to click the link.) But this property that topics are hard to understand the first time cannot be exclusive to math. For example, I don't know biology; still, I don't expect that articles that mention "mitochondria" should be rewritten so that "mitochondria" is replaced with "cell that generate energy". (Yes, I know that mitochondria is not a cell, but we have to keep it simple so that everyone understands.)
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Why are there so many references and notes sourced to R. Brown in this article? I am sure he is a fine topologist, but he isn't completely dominant in the field and a lot of his cited articles look to be on specialized topics not really suitable for a general overview of algebraic topology. It seems
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A great deal of pruning is needed. There is too much technical density here, and the list of notable algebraic topologists ought to be elsewhere. I think this article should be rewritten virtually from scratch by someone with a gift for exposition. A suitable reference at this level would be for
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I agree with the reply. I would also like to add that lots of topics in math have the property that you need some type of basic knowledge (master or sometimes research training) to be able to grasp them; if you try to rewrite them in a more "understandable" style a layman will still not understand,
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Must expand significantly by (at least) discussing the types of questions addressed by alg. top. and applications to other areas of maths, providing brief overviews of the main theories / techniques (such as homotopy, various (co-) homologies, stable homotopy,...) and having links to articles that
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This article uses too much terminology from the field that it is concerned with and is thus only of use and interest to people immersed in said field. It does not serve to introduce the topic or to explain it in any way to someone who does not have some prior training in the field. This makes it
299:"As another example, the top-dimensional integral homology group of a closed manifold detects orientability: this group is isomorphic to either the integers or 0, according as the manifold is orientable or not. "
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unsuited as an entry in a general encyclopedia and makes it more suited to a specialized mathematical encyclopedia. Please rewrite it to include more introductory explanations and examples.
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develop these further. As for the history section, a good source for that (if not most of the article!) is
Dieudonné's A History of Algebraic and Differential Topology 1900-1960 (
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I agree; I removed most of the material because it is not really good for an overview of algebraic topology, like you say, although it should probably be trimmed even more.
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Needs material on history, major sub-divisions and examples (such as the fundamental group); introduction and section on applications / major theorems needs expansion.
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closed manifold"). Perhaps you are confusing top homology with top cohomology?
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It is right that this should be a short article, directing readers quickly to
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I am not sure that it is as easily re-written as you suggest.
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I don't think it's an error (except that it doesn't say "
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Shouldn't that be the integers or the group of order 2?
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523:http://www.bangor.ac.uk/~mas010/nonab-a-t.html
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450:. Even better might be to merge the article
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