Riemannian manifolds not quasi-isometric to leaves in codimension one foliations (Q407802)

Every open manifold \(L\) of dimension greater than two admits complete Riemannian metrics \(g\) of bounded geometry such that \((L,g)\) is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Therefore no conditions on the local geometry of \((L,g)\) suffice to make it quasi-isometric to a leaf of such a foliation. The author introduces 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 Finiteness Lemma and a partial extension of the Novikov closed leaf theorem to higher dimensions.