Homological obstructions to local contractibility in noncollapsed Ricci limits

For every integer N≥4, we construct a compact noncollapsed Ricci limit X of closed N-manifolds with nonnegative Ricci curvature such that 0<ℋ^(N−2)(S_top(X))<∞, where S_top(X) is the nonmanifold locus. There is a compact subset Z⊂S_top(X) of positive (N−2)-dimensional Hausdorff measure such that, for every subset E⊂X with dim_ℋ E