Linked Questions
10 questions linked to/from Is there a complex structure on the 6-sphere?
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A paper to the question, if the six dimensional sphere is a complex manifold [duplicate]
for a few days a paper was published on arxiv.org with the title "The six dimensional sphere is a complex manifold": http://arxiv.org/PS_cache/math/pdf/0505/0505634v3.pdf
Because I am not able to ...
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Complex structure on $S^6$ gets published in Journ. Math. Phys
A paper by Gabor Etesi was published that purports to solve a major outstanding problem:
Complex structure on the six dimensional sphere from a spontaneous symmetry breaking
Journ. Math. Phys. 56, ...
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Is the complex structure of $\mathbb CP^n$ unique?
Let $\mathbb CP^n$ denotes the complex projective space of dimension $n$, we have a standard complex structure of $\mathbb CP^n$, and my question is: is this complex structure unique?
Or equivalently, ...
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Atiyah's May 2018 paper on the 6-sphere
A couple years ago Atiyah published a claimed proof that $S^6$ has no complex structure. I've heard murmurs and rumors that there are problems with the argument, but just a couple months ago he ...
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Does S^6 have the structure of an algebraic variety?
More accurately, the question should be: Is it known that $S^6,$ the 6-dimensional sphere, is $not$ a (proper) complex algebraic variety, or algebraic space? And is there a reference? It's easy to see ...
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What is the current understanding regarding complex structures on the 6-sphere?
In October 2016, Atiyah famously posted a preprint to the arXiv, "The Non-Existent Complex 6-Sphere" containing a very brief proof $S^6$ admits no complex structure, which I immediately read and ...
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Atiyah's paper on complex structures on $S^6$
M. Atiyah has posted a preprint on arXiv on the non-existence of complex structure on the sphere $S^6$.
https://arxiv.org/abs/1610.09366
It relies on the topological $K$-theory $KR$ and in ...
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An almost complex structure on the real $n$-sphere $S^n$
If $R\mathrel{:=}\mathbb{R}[x_1,\dotsc,x_{n+1}]/(x_1^2+\dotsb+x_{n+1}^2-1)$ and $S^n\mathrel{:=}\operatorname{Spec}(R)$ is the real $n$-spere, a classical result of Borel and Serre says that the only ...
user122276
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Atiyah's paper "Non-existent complex 6-sphere"
I'm trying to understand the main idea of Atiyah's proof (https://arxiv.org/abs/1610.09366). Although there were discussions on MO year ago I couldn't find answers to my questions.
Consider the ...
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PDE obtained while trying to construct a complex structure
Upon reading this answer to this question, the last paragraph mentions the following. "Requiring the [almost complex] structure to be integrable corresponds to a certain PDE for this map." ...
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