Talk:Milnor conjecture (Ricci curvature)

Link to disambiguation

@Jlwoodwa: It is extremely difficult for a non-topologist to tell one Milnor conjecture from another. They are all reasonably important, and currently named confusingly (I have retained the "Ricci" disambiguation in this article as it was used already in the List of things named after John Milnor). In my opinion, the link to Milnor conjecture (disambiguation) in all three articles is therefore critical. I would prefer to use {{otheruses}} in the spirit of WP:IAR; if this is not acceptable, let's figure some other way. {{about}} would work, but it seems to me as a clumsier way to achieve the same result. Викидим (talk) 01:33, 16 May 2024 (UTC)[reply]

@Викидим: I think {{for}}/{{about}}/{{distinguish}} are more appropriate when the title is unambiguous but still easily confused with similarly-titled articles. For instance, articles named "Treaty of Paris (some year)" have a hatnote saying "For other treaties of Paris, see Treaty of Paris (disambiguation)." Maybe something like "For other conjectures by Milnor," would work here? jlwoodwa (talk) 01:40, 16 May 2024 (UTC)[reply]

I like your {{for}} suggestion. Викидим (talk) 01:41, 16 May 2024 (UTC)[reply]

Disproven?

The work of Brue et al has yet to be peer reviewed and published (17/5/2024). I don't think it is correct to claim that the counter-examples, claimed in the Quanta article, are established fact. This article needs to be a bit less hasty in making claims. Two other things: The conjecture, according to Quanta, has been PROVED for 3 or fewer dimensions. This is a fact (I assume), and should ...OBVIOUSLY...be mentioned. You may *think* it has been mentioned, but does "for the non-trivial cases of two dimensions and three dimensions" mean that? It requires the reader to know what is and isn't a "trivial" case. (for instance, isn't a sphere a trivial 2-dimensional manifold? Why not? etc.) The other thing is it also seems obvious to me that if "Milnor Conjecture" is commonly used term for more than one idea, especially if they've got their own Wikipedia articles, that that fact should be made explicitly and upfront. It should, imho, be the first or 2nd sentence of the lead. That is either A) "The Milnor Conjecture on Ricci Curvature ... . Note that two other of his conjectures are also described as 'The Milnor Conjecture' (see ...)" or, more simply B) John Milnor made several well-known conjectures that share the same name. This article is about his conjecture concerning Ricci curvature, for the others see (Milnor Conjecture - disambiguation). I guess my point is that while "for other Milnor conjectures, see..." as a preface note may not be read and I suspect the issue is important enough to justify its inclusion in the body of the article. My two cents, fwiw. (At the very least, if it's decided to keep the current form, it should use Conjecture rather than conjecture since what is being distinguished is the versions having the same proper name, Milnor Conjecture.)72.16.97.19 (talk) 16:16, 17 May 2024 (UTC)[reply]

Dear colleague, thank you for taking time to make a long comment. Few notes:

work of Brue et al has yet to be peer reviewed and published - yes, it is not published in a peer-reviewed journal at this point, as far as I know. However, the researchers are known, the result in novel, so many eyes of the actual peers have certainly already looked at it. The result is already cited in works of independent researchers. Cepelewicz certainly contacted few peers, too (she says so). Feel free to propose better language.
conjecture, according to Quanta, has been PROVED for 3 or fewer dimensions. This is a fact (I assume), and should ...OBVIOUSLY...be mentioned - the statement of fact is true, and the fact actually is already mentioned in the very first paragraph.
"Milnor Conjecture" is commonly used term for more than one idea, especially if they've got their own Wikipedia articles, that that fact should be made explicitly and upfront. Yes, and this is done precisely as the Wikipedia style suggests it: through a {{for}} construct.
it should use Conjecture - I have kept the use of non-capital "c" from the other "Milnor conjecture" articles. This is the typical spelling for these objects in Wikipedia, cf. Pythagorean theorem.

Викидим (talk) 17:26, 17 May 2024 (UTC)[reply]

In two dimensions M2 has finitely generated fundamental group as a consequence that if Ric > 0 {\displaystyle \operatorname {Ric} >0} for noncompact M 2 {\displaystyle M^{2}}, then it is flat or diffeomorphic to R 2 {\displaystyle \mathbb {R} ^{2}}, by work of Cohn-Vossen from 1935.

I suspect that this should be $Ric\geq 0$ rather than $Ric>0$ , right?—Cheongnyangni-dong (talk) 13:39, 25 December 2024 (UTC)[reply]