Displaying similar documents to “Codimension one minimal foliations and the fundamental groups of leaves”

The diffeomorphism group of a Lie foliation

Gilbert Hector, Enrique Macías-Virgós, Antonio Sotelo-Armesto (2011)

Annales de l’institut Fourier

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We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus T n , n ≥ 2 . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are ± Id and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for T 2 , P. Iglesias...

Flows of flowable Reeb homeomorphisms

Shigenori Matsumoto (2012)

Annales de l’institut Fourier

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We consider a fixed point free homeomorphism h of the closed band B = ℝ × [ 0 , 1 ] which leaves each leaf of a Reeb foliation on B invariant. Assuming h is the time one of various topological flows, we compare the restriction of the flows on the boundary.

Smoothability of proper foliations

John Cantwell, Lawrence Conlon (1988)

Annales de l'institut Fourier

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Compact, C 2 -foliated manifolds of codimension one, having all leaves proper, are shown to be C ∞ -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class C ∞ . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class C r and of class C r + 1 for every nonnegative integer r .

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

Paul A. Schweitzer (2011)

Annales de l’institut Fourier

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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....