Abstract In any dimension n+1 4 n + 1 ≥ 4 we construct a sequence of closed (n+1) (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.
Maximo et al. (Sat,) studied this question.