Wikipedia:Peer review/Mayer–Vietoris sequence/archive1

Mayer–Vietoris sequence

• A script has been used to generate a semi-automated review of the article for issues relating to grammar and house style; it can be found on the automated peer review page for November 2008.

This peer review discussion has been closed.
I've listed this article for peer review because this is my first article, and I want to get it to Good Article status.

Thanks, GeometryGirl (talk) 11:55, 29 November 2008 (UTC)

Comments from Jakob.scholbach I think, overall the article is a good asset, written clearly and inviting to read. Some minor issues:

• Lead section: "as the groups of singular chains" -- should omit the "as"
• Also, the lead section should summarize the article. This article is relatively short, but in principle every section of the article should be represented by the lead appropriately.
• Mathematical markup: I personally prefer using usual text whereever possible. For the long exact sequences LateX is fine, I guess, but

Thus $\displaystyle \partial x=\partial (u+v)=0$ so that $\partial u=-\partial v$.

could be rewritten as

Thus ∂x = ∂(u + v) = 0

which looks neater, IMO. Check out this list of characters if you need.

*Another thing: in mathematical text, minus should not be typed by a hyphen but by −, which gives a longer dash: −

• The tag has to be dealt with. (In general referencing is fine, but the Bott-Tu reference should be placed next to the other ones. A helpful resource is zeteo.info, which contains many mathematics books references, in this case it is at [1]).
• In the second homological version long exact sequence, the indices are somehow messed up (i_* would go from H(A, C) to H(X,Y), I guess). It would also be good to name the maps (already for the first one).
• What does "chain groups" mean (derivation section)? A redlink is not so helpful, a short explanation is better.
• What does C_n (A + B) mean?
• Examples: k-sphere should be wikilinked.
• The hemispheres are not complementary, as pointed out later.

Since you also candidate for Good Article status, some other remarks that I think would be nice to be adressed for the article being "good":

• There is no history information at all. At least mentioning whether M & V proved the thing should be done.
• An image would be really good (also a formal GA criterion, I think). The sphere-case should be no big deal to draw.
• Perhaps one more advanced example would be nice. Currently the article reads a bit like a introductory textbook section.
• What about generalizations and related notions? E.g. what about other topologies (e.g. Nisnevich topology). Also other types of (co)homology would be good, e.g. etale cohomology (actually pretty much any cohomology theory, right?) Jakob.scholbach (talk) 22:12, 2 December 2008 (UTC)

I agree with Jakob that the article needs images. This is a priority, in my view, and I've added this point to the maths rating. Geometry guy 21:37, 6 December 2008 (UTC)

Thanks for the comments. I know nothing about creating pictures. I have ideas about pictures but I feel powerless... For example, I would like to illustrate the boundary map in the homological case. I want a two-dimensional space (a torus would be nice) decomposed as two overlapping subspaces A and B with a 1-cycle looping around and decomposed as the sum of two cycles lying wholly in A and B with the relevant common boundary represented. Any help? GeometryGirl (talk) 22:31, 6 December 2008 (UTC)

I'm not an image expert, but Inkscape usually does a good job. Jakob.scholbach (talk) 16:04, 7 December 2008 (UTC)

Update: The images chosen in the article are better than nothing, but a drawing that really shows the two overlapping(!) hemispheres would be better then just cutting a billiard ball into halves. The current images don't illustrate the use of the sequence too well. Hatchers book (Hatcher, Allen (2002), Algebraic topology, Cambridge University Press, ISBN 978-0-521-79540-1) might give some ideas... Jakob.scholbach (talk) 16:08, 7 December 2008 (UTC)

I think the article could use a bit of discussion about possible generalizations, the uses of such sequences, and how they apply to the field of topology as a whole. I'm far from an expert on topology, so apologies if these are already here. RayAYang (talk) 20:43, 5 December 2008 (UTC)