Talk:Mayer–Vietoris sequence/GA1

GA Review

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Well-written

Extremely well written in general. I have made a few minor adjustments and have some further comments by section. A general note about displayed equations: should they be punctuated properly? For example if they occur at the end of a sentence, should there be a full-stop?

I prefer removing all punctuation, I find it obtrusive. Many authors do that (e.g. Hatcher). GeometryGirl (talk)

Lede

• A wikilink for "singular (co)homology"?

Done GeometryGirl (talk)

• Consider removing "so" in "So carefully choosing ..." to avoid the repeated word.

Done GeometryGirl (talk)

• The M-V sequence "holds" in ... Can a sequence hold? Or would "is valid in" or "can be used in" be better?

The word 'result' or 'theorem' is implicit: "The M-V sequence result holds..." But maybe changing is better. GeometryGirl (talk)

• I think it would be helpful to have a brief sentence (if possible) about what homology and cohomology is and why they are useful to put the M-V sequence into context.

I've made it clear that it was the "invariant" we were interested in. GeometryGirl (talk)

• The word "patch" is used informally. But might a reader wonder whether what it is?

There are different ways of patching, each specific to the kind of space studied. The different spaces are listed in the Motivation section. GeometryGirl (talk)

Background and motivation

• Wikilink "exact sequences" (only L.E.S. is linked in the lede)

Done GeometryGirl (talk)

• Grammar error? "This does not allow in general to completely compute ..." The passive is needed here.

Could you change it for me please? I don't know English grammar. GeometryGirl (talk)

Done, but then, I'm not a mathematician - might be worth checking to see if that's what you intended to say. Jarry1250 (talk) 17:35, 30 December 2008 (UTC)

• Replace "a theorem such as that of Mayer and Vietoris" with "the Mayer–Vietoris sequence"? It is not called a theorem before this point.

This is interesting since the M-V sequence is a theorem. It is not any old sequence, it is exact. That's the theorem. GeometryGirl (talk)

Basic versions for singular homology

• It wasn't completely obvious what the inclusion maps i,j,k,l were

Added the explicit maps. GeometryGirl (talk)

• Link "abelianized" or "abelianization" to abelian?

Done GeometryGirl (talk)

Further discussion

• Funny grammar: "... for a continuous map f from X1 = A1∪B1 to X2 = A2∪B2 with f(A1) ⊂ A2 and f(B1) ⊂ B2 then f induces a map f* between ..."

Hopefully corrected. GeometryGirl (talk)

History

This section seems out of place here. Could it be incorporated into the "background" section higher up?

Done, thanks for the suggestion. GeometryGirl (talk)

Factually accurate and verifiable

I find the references perfectly adequate. It is of course great that the major source is freely available! It might be preferable to link the short footnotes to the main references. (I have done this for Hatcher as a start.)

I've added the links. GeometryGirl (talk)

Broad in its coverage

The article provides comprehensive coverage of the topic. I feel however that a little more background is required, both in the lede and in the "background" section. It would be nice if the first paragraph was accessible to even a non-mathematician; at the moment it is not. I know from experience that this is very hard, but could some attempt be made to explain why the M-V sequence is important and useful, without using any kind of technical language such as "algebraic invariants" or "homology"?

Then perhaps in the second paragraph there could be a little more info on homology and cohomology. Interested readers can of course click the link, but there should be just enough in this article to give some context.

Could there be included some details about other related areas of mathematics? For example, what other tools are available for computing the homology groups and how do they compare to the M-V sequence?

I know what I am asking is probably difficult verging on impossible ;)

I'll think about this. GeometryGirl (talk)

Neutral

Fine.

Stable

Fine.

Images

This article has some fantastic images and I commend the work that has gone into them. They really help to explain and clarify the subject. The hand-drawn diagram is also excellent and clear. I never knew that you could glue two mobius strips together to make a Klein bottle!

Yes, this is thanks to RobHar's great job in converting my drawings. The hand-drawn diagram will hopefully also be converted shortly to make things look more professional and consistent. GeometryGirl (talk)

All images are properly licensed and tagged.

In conclusion, congratulations on the editors who have created such a good article. I await some input from others who are more familiar with the subject. Martin 12:21, 21 December 2008 (UTC)

Many thanks Martin! GeometryGirl (talk)

Follow-up

Well it seems I will have to manage without other input. I am satisfied that all the minor points have been settled. In addition there have been some significant improvements to the lede. I still think this could probably be made more accessible, which would be important if this article was ever to make the main page (which I hope it does one day). I am now going to list this as a good article. Martin 22:04, 30 December 2008 (UTC)