Wikipedia:WikiProject Mathematics/A-class rating/Homotopy groups of spheres

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I don't think there is consensus to promote to A-class, but the article seems close. Perhaps another nomination in a month or two, after the edits

Homotopy groups of spheres (edit | talk | history | links | watch | logs) review
I believe that this article now meets the standard for A-Class. In particular, I believe it is comprehensive, factually accurate and verifiable, and would like experts to check this and point out areas for improvement. However, I am mainly nominating here to ask for input from members of the Mathematics WikiProject (and others) on the presentation, balance, and accessibility of the article. Is the technical material accessible enough for an article of this nature? Is there too much technical material? In what ways could the presentation could be improved? How broad is the target audience? I hope this will stimulate some useful discussion.
Nominated by: Geometry guy 18:43, 5 November 2007 (UTC)[reply]

• I like the article a lot, but I think it can still be improved, especially by adding material about some other current approaches, not yet mentioned in the article. If there is some interest in that, I can give it a shot, and see how it goes. (I'm not a member of MWP, so I'm not quite sure how one gets involved in these discussions...) Turgidson 03:40, 15 November 2007 (UTC)[reply]

Thanks for commenting. Comments from everyone are most welcome here, on the

mathematics project talk page, and on the article talk page — there is certainly no membership requirement! What material do you think is missing? Geometry guy 19:53, 15 November 2007 (UTC)[reply

]

Computing the homotopy groups of S^2 via braid groups. I could add a section on that -- it would tie up this subject to a whole slew of others ones (including links in S^3 and combinatorial group theory). It's just that I need some time to do a more-or-less reasonable job, and it would need some pictures to make it look nice, so I'm a bit nervous to invest too much time and effort without knowing whether there would be some interest in this (I'm in an especially funky mood after some upsetting experiences at certain recent CFD/DRVs). Any thoughts? Turgidson 20:25, 15 November 2007 (UTC)[reply]

This sounds great to me. In particular, we desperately need a good image to associate with π₃(S²). I appreciate your mood: believe me, Homotopy groups of spheres is much more fun than certain CfD/DRV's that we don't need to mention! And it has great editors (KSmrq, R.e.b., Jakob Scholbach etc.) working on it too. Geometry guy 20:35, 15 November 2007 (UTC)[reply]

Thanks for the encouragement. OK, I'll give it a shot, then, just please have a bit of patience, it may not be completely polished right away, as I will need to do it in between other things I'm doing at the same time, both on and off WP. Let's continue the discussion on the talk page, once I get off the ground. Turgidson 20:42, 15 November 2007 (UTC)[reply]

I read through the first several sections in detail, and skimmed that later ones. It's a good article, although (perhaps unavoidably) only accessible to someone with a decent ability to handle blue links and notation. Concrete areas of possible improvement:

• Add some images to the "n-sphere" section near the beginning. For example suspensions should be able to be illustrated without too much effort.
• In the section "general theory", be more clear that the patterns are actually provable and continue indefinitely. This is implied but maybe not clear to a naive reader.
• The "applications" section is likely to be of interest; specific references for more of the bullet points would be nice.

For someone who already has an undergrad background, or who is willing to accept undefined terms to get a bigger picture, this is a very nice article to read. — Carl (