Macroscopic-dimension conjecture for universal covers of positive-scalar-curvature manifolds

Establish whether the universal cover of every closed n-manifold with positive scalar curvature has macroscopic dimension at most n−2.

Background

This conjecture is another codimension-two prediction attributed to Gromov. It concerns the large-scale dimension of the universal cover of a closed manifold carrying a positive-scalar-curvature metric. The paper cites partial results but does not state a general resolution, so the conjecture is included as an explicitly identified unresolved problem.