There exist two sequences of closed 4-manifolds with nonnegative Ricci curvature, bounded diameter and volume, which converge to the same Gromov-Hausdorff limit yet have fundamental groups Z/2Z and trivial.
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Instability of the fundamental group for non-collapsed Ricci-limits
There exist two sequences of closed 4-manifolds with nonnegative Ricci curvature, bounded diameter and volume, which converge to the same Gromov-Hausdorff limit yet have fundamental groups Z/2Z and trivial.