Timeline for Atiyah's paper "Non-existent complex 6-sphere"
Current License: CC BY-SA 3.0
11 events
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Jun 13, 2018 at 15:52 | comment | added | Danu | It appears that Atiyah has published another (attempt at a) proof in an article which is not on arXiv, but appears in the book "Foundations of Mathematics and Physics One Century after Hilbert", which was very recently released. | |
Dec 12, 2017 at 7:16 | history | edited | Max Borovkov | CC BY-SA 3.0 |
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Dec 11, 2017 at 11:55 | comment | added | Neil Strickland | (1) Part of Bott periodicity is that $\Omega^4(\mathbb{Z}\times BO)=\mathbb{Z}\times BSp$ and $\Omega^4(\mathbb{Z}\times BSp)=\mathbb{Z}\times BO$, so $KSp$ is the same as $KO$ up to a shift. (2) Atiyah is implicitly using $K$-theory with compact supports, for which $K(U)=\widetilde{K}(U\cup\{\infty\})$ almost by definition. And $S^6\simeq\mathbb{R}^6\cup\{\infty\}$. | |
Dec 11, 2017 at 0:16 | comment | added | YangMills | Honestly I cannot even see which part of Atiyah's argument would supposedly use that the almost complex structure is integrable. | |
Dec 10, 2017 at 20:56 | history | edited | YCor |
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Dec 10, 2017 at 20:27 | comment | added | Max Borovkov | @YCor, ok, I asked the last question only to have an updated information. However, first three questions might be still open. | |
Dec 10, 2017 at 20:15 | comment | added | Denis Nardin | I'm going out on a limb and say that the paper does not contain an actual proof. I don't know whether the author plans to publish a follow up with more details or not, but for now I still consider the problem open. | |
Dec 10, 2017 at 20:11 | comment | added | YCor | The last question "is this proof accepted as true in math society" makes a duplicate of mathoverflow.net/questions/263301. I'd suggest to stick to questions 1,2,3. | |
Dec 10, 2017 at 20:07 | comment | added | David Roberts♦ | You should regard that paper as a sketch of a claimed proof that has not since appeared. | |
Dec 10, 2017 at 20:06 | comment | added | YCor | Links to past MO discussions: mathoverflow.net/questions/1973, mathoverflow.net/questions/253577, mathoverflow.net/questions/263301 | |
Dec 10, 2017 at 20:00 | history | asked | Max Borovkov | CC BY-SA 3.0 |