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arXiv · 2609.26706

A Conditional Oka Complex Structure of the Six-Sphere

Zhangchi Chen
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Abstract

Alpöge constructs a compact complex threefold $Y$ fibred over $\mathbb{P}^1$ by complex two-tori away from three special points. We prove that $Y$ is an Oka manifold. The proof applies to every admissible period parameter with the same logarithmic twists and cusp gluing. If one also accepts the identification of the underlying smooth manifold with $S^6$ in Alpöge's Theorem~8.1, then the six-sphere admits an Oka complex structure. This topological identification is not used in the Oka proof.

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Zhangchi Chen. 2026-09-22. A Conditional Oka Complex Structure of the Six-Sphere. https://arxiv.org/abs/2609.26706

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