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I'm writing a paper that, rather unexpectedly, needs the Poincaré conjecture for one of the results. (The paper has almost nothing to do with differential geometry!)

The conjecture was famously proved at the beginning of the century by Perelman, in a series of three papers. Unfortunately, I'm not a differential geometer, and I fear that if I read his papers I won't understand anything or be able to pinpoint in which one the conjecture is solved.

I'm sure that if I just write "the Poincaré conjecture, due to Perelman" in my paper everybody will understand what I'm talking about. But it still feels "normal" to cite something. So: what should I cite? Nothing? One of the three papers? All three of them? Something else?

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  • $\begingroup$ Out of curiosity - why does the conjecture pop up? $\endgroup$
    – Arrow
    Commented Jul 26, 2016 at 8:20
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    $\begingroup$ @Arrow I have a proof that works for all closed simply connected manifolds of dimension at least 4, and the proposition is obvious for spheres for other reasons. $\endgroup$
    – Najib Idrissi
    Commented Jul 26, 2016 at 8:21
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    $\begingroup$ @post.as.a.guest, that doesn't seem to be the case at all. It appears that the OP wants to assert that his theorem is true for all simply connected manifolds, and needs the fact that every closed, simply connected 3-manifold is a sphere. That is exactly the statement of the Poincaré conjecture. $\endgroup$
    – HJRW
    Commented Jul 26, 2016 at 12:19
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    $\begingroup$ In any event "the Poincaré conjecture, due to Perelman" (as the OP text suggests) is a dubious linguistic construction/shorthand, as the Poincaré conjecture as such is due to Poincaré, with the proof of it being due to Perelman (and others, if you wish). $\endgroup$
    – post.as.a.guest
    Commented Jul 26, 2016 at 12:42
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    $\begingroup$ @post.as.a.guest: right, it's an unfortunate quirk that even once a conjecture is proven, it can continue to be known by the now-inadequate title it has borne. "The Poincaré Conjecture" is, unfortunately, used here as the name of the theorem proved by Perelman. If it was called "Perelman's Theorem" then we wouldn't have this fuss about whether one says, "we know this by PT" or "we know this by the proof of PT". The former alone would be sufficient to imply we're taken that it's proven. $\endgroup$
    – Steve Jessop
    Commented Jul 26, 2016 at 16:37

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I think it is customary to cite at least the first two papers ("The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds"). See this for an example. Together they imply the full geometrization conjecture.

The shortest proof of "just Poincare" involves the third paper, but I guess that's beyod the point.

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    $\begingroup$ I would also consider citing the monographs of Morgan--Tian and Kleiner--Lott. $\endgroup$
    – HJRW
    Commented Jul 26, 2016 at 12:15
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    $\begingroup$ Cite the Perelman papers directly and in parentheses, say "also, see..." and cite the other expositions of the proof. $\endgroup$
    – Deane Yang
    Commented Jul 26, 2016 at 18:29

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