  In this note we relate the geometric notion of fill radius with the
fundamental group of the manifold. We prove: ''Suppose that a closed Riemannian
manifold M satisfies the property that its universal cover has bounded fill
radius. Then the fundamental group of M is virtually free.'' We explain the
relevance of this theorem to some conjectures on positive isotropic curvature
and 2-positive Ricci curvature.
