This research constructs Riemannian manifolds with positive Ricci curvature, revealing minimal hypersurfaces with high Betti numbers.
In any dimension n+1≥ 4 we construct a sequence of closed $(n+1)$-dimensional Riemannian manifolds with positive Ricci curvature admitting embedded two-sided minimal hypersurfaces such that the following hold: (i) any such hypersurface has Morse index one; (ii) the first Betti numbers of the hypsersurfaces are not uniformly bounded along the sequence.
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Máximo et al. (2025) studied this question.
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