It is known that $S^6$ admits an almost complex structure which is not integrable, recently Michael Atiyah posted a proof of non-existent of a complex structure on this sphere.
I am curious now about the other spheres i.e what about $S^{4}$ and $S^{2n}$ for $n\geq4$?
Is there any good introduction reference where one at the undergraduate level can read about that?
