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Closure of the Oka-1 Class under Strong Dominability

Ascertain whether the class of Oka‑1 manifolds is closed under strong dominability.

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Background

After showing that closing the Oka class under strong dominability preserves LSAP and hence Oka‑1, the authors point out that the analogous closure property for the Oka‑1 class itself is also unsettled.

Addressing this would clarify the structural stability of the Oka‑1 property under local domination maps and strengthen the functorial framework around Oka‑type properties.

References

It is an interesting open question whether the class of Oka manifolds is closed with respect to strong dominability (or merely Hausdorff-local). The question is open for the class of Oka-1 manifolds as well.

— Oka-1 manifolds: New examples and properties (2402.09798 - Forstneric et al., 15 Feb 2024) in Section 1 (Introduction), following Theorem 1.11