Displaying similar documents to “A type of non-equivalent pseudogroups. Application to foliations”

On foliations in Sikorski differential spaces with Brouwerian leaves

Włodzimierz Waliszewski (1991)

Annales Polonici Mathematici

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The class of locally connected and locally homeomorphically homogeneous topological spaces such that every one-to-one continuous mapping of an open subspace into the space is open has been considered. For a foliation F [3] on a Sikorski differential space M with leaves having the above properties it is proved that for some open sets U in M covering the set of all points of M the connected components of U ∩ L̲ in the topology of M coincide with the connected components in the topology...

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....

Continuity of projections of natural bundles

Włodzimierz M. Mikulski (1992)

Annales Polonici Mathematici

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This paper is a contribution to the axiomatic approach to geometric objects. A collection of a manifold M, a topological space N, a group homomorphism E: Diff(M) → Homeo(N) and a function π: N → M is called a quasi-natural bundle if (1) π ∘ E(f) = f ∘ π for every f ∈ Diff(M) and (2) if f,g ∈ Diff(M) are two diffeomorphisms such that f|U = g|U for some open subset U of M, then E(f)|π^{-1}(U) = E(g)|π^{-1}(U). We give conditions which ensure that π: N → M is continuous. In particular,...

A topological version of Bertini's theorem

Artur Piękosz (1995)

Annales Polonici Mathematici

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We give a topological version of a Bertini type theorem due to Abhyankar. A new definition of a branched covering is given. If the restriction π V : V → Y of the natural projection π: Y × Z → Y to a closed set V ⊂ Y × Z is a branched covering then, under certain assumptions, we can obtain generators of the fundamental group π₁((Y×Z).