Riemannian manifolds not quasi-isometric to leaves in codimension one foliations
Annales de l’institut Fourier2011Vol. 61(4), pp. 1599–1631
Citations Over TimeTop 16% of 2011 papers
Abstract
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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