# Riemannian manifolds not quasi-isometric to leaves in codimension one foliations

Paul A. Schweitzer^{[1]}

- [1] Depto. de Matemática, Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, RJ 22453-900, Brasil

Annales de l’institut Fourier (2011)

- Volume: 61, Issue: 4, page 1599-1631
- ISSN: 0373-0956

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topSchweitzer, Paul A.. "Riemannian manifolds not quasi-isometric to leaves in codimension one foliations." Annales de l’institut Fourier 61.4 (2011): 1599-1631. <http://eudml.org/doc/219796>.

@article{Schweitzer2011,

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.},

affiliation = {Depto. de Matemática, Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, RJ 22453-900, Brasil},

author = {Schweitzer, Paul A.},

journal = {Annales de l’institut Fourier},

keywords = {codimension one foliation; Reeb component; non-leaf; geometry of leaves; bounded homology property; quasi-isometry; closed leaf theorem},

language = {eng},

number = {4},

pages = {1599-1631},

publisher = {Association des Annales de l’institut Fourier},

title = {Riemannian manifolds not quasi-isometric to leaves in codimension one foliations},

url = {http://eudml.org/doc/219796},

volume = {61},

year = {2011},

}

TY - JOUR

AU - Schweitzer, Paul A.

TI - Riemannian manifolds not quasi-isometric to leaves in codimension one foliations

JO - Annales de l’institut Fourier

PY - 2011

PB - Association des Annales de l’institut Fourier

VL - 61

IS - 4

SP - 1599

EP - 1631

AB - 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.

LA - eng

KW - codimension one foliation; Reeb component; non-leaf; geometry of leaves; bounded homology property; quasi-isometry; closed leaf theorem

UR - http://eudml.org/doc/219796

ER -

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