Shioya–Yamaguchi's Alexandrov sphere conjecture

Let $Y^3_\infty$ be a $3$-dimensional compact, simply connected, non-negatively curved Alexandrov space without boundary, and suppose that $Y^3_\infty$ is a topological manifold. Shioya–Yamaguchi's conjecture. Then $Y^3_\infty$ is homeomorphic to a sphere. This conjecture concerns the topology of diameter-collapsed limits in the study of collapsing $3$-manifolds; the source gives no evidence of its resolution.