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Given a compact Riemannian manifold, of dimension between 3 and 7, withboundary, we adapt Song's method in Song (2019) to the free boundary case toshow that the Morse index of a free boundary minimal hypersurface growslinearly with the sum of its Betti numbers, where the constant of growthdepends on the area of the free boundary minimal hypersurface in question.

Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments