An application of a theorem of Huber in holomorphic foliation theory

Hans-Jörg Reiffen

Displaying similar documents to “An application of a theorem of Huber in holomorphic foliation theory”

Foliations with complex leaves

Giuseppe Tomassini (1995)

Banach Center Publications

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Finite determinacy of dicritical singularities in $(ℂ^{2}, 0)$

Gabriel Calsamiglia-Mendlewicz (2007)

Annales de l’institut Fourier

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For germs of singularities of holomorphic foliations in $(ℂ^{2}, 0)$ which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.

The $C^{1}$ invariance of the algebraic multiplicity of a holomorphic vector field

Rudy Rosas (2010)

Annales de l’institut Fourier

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We prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by $C^{1}$ equivalences.

Foliations with Degenerate Gauss maps on $ℙ^{4}$

Thiago Fassarella (2010)

Annales de l’institut Fourier

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We obtain a classification of codimension one holomorphic foliations on $ℙ^{4}$ with degenerate Gauss maps.

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

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Let $ℱ$ be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold $M$ . We show that if the fundamental group of each leaf of $ℱ$ is isomorphic to $Z$ , then $ℱ$ is without holonomy. We also show that if $π_{2} (M) ≅ 0$ and the fundamental group of each leaf of $ℱ$ is isomorphic to $Z^{k}$ ( $k \in Z_{\geq 0}$ ), then $ℱ$ is without holonomy.

A type of non-equivalent pseudogroups. Application to foliations

Jesús A. Alvarez López (1992)

Annales Polonici Mathematici

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A topological result for non-Hausdorff spaces is proved and used to obtain a non-equivalence theorem for pseudogroups of local transformations. This theorem is applied to the holonomy pseudogroup of foliations.

On Lie algebras of vector fields related to Riemannian foliations

Tomasz Rybicki (1993)

Annales Polonici Mathematici

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Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.

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....