English

The Non-Existent Complex 6-Sphere

Differential Geometry 2016-11-04 v2

Abstract

The possible existence of a complex structure on the 6-sphere has been a famous unsolved problem for over 60 years. In that time many "solutions" have been put forward, in both directions. Mistakes have always been found. In this paper I present a short proof of the non-existence, based on ideas developed, but not fully exploited, over 50 years ago. The only change in v2. is in section 3, where the notation has been clarified.

Cite

@article{arxiv.1610.09366,
  title  = {The Non-Existent Complex 6-Sphere},
  author = {Michael Atiyah},
  journal= {arXiv preprint arXiv:1610.09366},
  year   = {2016}
}
R2 v1 2026-06-22T16:35:43.204Z