Ricci curvature and minimal hypersurfaces with large Betti numbers
Abstract
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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