All Questions

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 ...

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 ...

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 ...

I'm confused with working out the Chern character in the following special setting. Let $E$ be a spinor bundle $$S=P_{Spin(2n)}(S^{2n})\times_\rho \mathbb{C}^{2n}$$ over sphere $S^{2n}$, where $\rho$ ...