Chern's contribution to the Hopf problem: an exposition based on Bryant's paper

TL;DR

This paper explains Chern's theorem proving that the 6-sphere cannot have an omega-compatible almost complex structure, providing a detailed exposition based on Bryant's work, mainly summarizing existing literature.

Contribution

It offers a comprehensive exposition of Chern's theorem on S^6's non-existence of omega-compatible almost complex structures, based on Bryant's paper, without presenting new results.

Findings

S^6 admits no omega-compatible almost complex structures

The paper clarifies Chern's theorem and its proof

Provides historical and mathematical context for the theorem

Abstract

We give a comprehensive account of Chern's Theorem that S^6 admits no omega-compatible almost complex structures. No claim to originality is being made, as the paper is mostly an expanded version of material already in the literature. This article extends the talks that both authors gave in Marburg during the conference "(Non)existence of complex structures on S^6" in April 2017.