  Every open manifold L of dimension greater than one has complete Riemannian
metrics g with bounded geometry such that (L,g) is not quasi-isometric to a
leaf of a codimension one foliation of a closed manifold. Hence no conditions
on the local geometry of (L,g) suffice to make it quasi-isometric to a leaf of
such a foliation. We introduce the `bounded homology property', a semi-local
property of (L,g) that is necessary for it to be a leaf in a compact manifold
in codimension one, up to quasi-isometry. An essential step involves a partial
generalization of the Novikov closed leaf theorem to higher dimensions.
