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Register a new userRiemannian manifolds not quasi-isometric to leaves in codimension one foliations
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Authors
Paul A. Schweitzer
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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.
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