On the history of the Hopf problem

Abstract

This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on $S^6$?" This unsolved mathematical question was the subject of the Conference "MAM 1 $-$ (Non-)Existence of Complex Structures on $S^6$", which took place at Philipps-Universität Marburg, Germany, between March 27th and March 30th, 2017.

7 pages, contains some open questions. Comments are welcome!

References in corpus (6)

• Notes on $G_2$: The Lie algebra and the Lie group
• Almost complex structures on spheres
• Hodge numbers of a hypothetical complex structure on $S^6$
• The complex geometry of a hypothetical complex structure on $S^6$
• Chern's contribution to the Hopf problem: an exposition based on Bryant's paper
• Non-existence of orthogonal complex structures on the round 6-sphere