Exotic smoothings under the curvature hypotheses

Determine whether the curvature hypotheses of nonnegative Ricci curvature and nonnegative quadratic orthogonal bisectional curvature, or the stronger nonnegative bisectional-curvature condition, exclude exotic smoothings of real four-dimensional Euclidean space.

Background

The paper proves that a complete noncompact Kähler surface satisfying nonnegative Ricci curvature and nonnegative quadratic orthogonal bisectional curvature is contractible when it is simply connected at infinity, and consequently is homeomorphic to real four-dimensional Euclidean space. Because real dimension four admits exotic smooth structures, the paper notes that contractibility, simple connectivity at infinity, and ordinary Steinness do not determine the smooth structure. The unresolved issue is whether the curvature assumptions rule out such exotic smoothings.