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Let $\mathcal{F}$ be a transversely orientable codimension one minimalfoliation without vanishing cycles of a manifold $M$. We show that if thefundamental group of each leaf of $\mathcal{F}$ has polynomial growth of degree$k$ for some non-negative integer $k$, then the foliation $\mathcal{F}$ iswithout holonomy.

Codimension one minimal foliations whose leaves have fundamental groups with the same polynomial growth