Talk:Algebraic topology

Unsuitable as a general encyclopedic entry

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 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.

41.204.193.43 (talk) 12:19, 25 May 2009 (UTC)

I am not sure that it is as easily re-written as you suggest. — Preceding unsigned comment added by 31.53.52.243 (talk) 08:30, 13 July 2017 (UTC)

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, 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.) 84.55.110.150 (talk) 20:49, 23 November 2023 (UTC)

Correction

I'd just like to point out an error:

"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. "

Shouldn't that be the integers or the group of order 2?

87.194.112.50 (talk) 16:10, 4 October 2010 (UTC)

I don't think it's an error (except that it doesn't say "connected closed manifold"). Perhaps you are confusing top homology with top cohomology?

Ambrose H. Field (talk) 22:56, 17 January 2011 (UTC)

R. Brown

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 like undue weight and possible ref spamming. --Mark viking (talk) 04:38, 18 October 2013 (UTC)

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.Brirush (talk) 12:57, 18 October 2013 (UTC)

Assessment comment

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Comment(s)

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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. Tompw 18:27, 5 October 2006 (UTC) 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 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 (ISBN 081763388X). Stca74 21:43, 14 May 2007 (UTC) 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 instance M. A. Armstrong's book "Basic Topology". It is right that this should be a short article, directing readers quickly to Euler Characteristic, Homology theory, Homotopy, Fundamental group. Even better might be to merge the article Homology theory into a newly-rewritten Algebraic topology. Ambrose H. Field (talk) 11:11, 21 November 2009 (UTC)

Last edited at 11:11, 21 November 2009 (UTC). Substituted at 01:45, 5 May 2016 (UTC)

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