Displaying similar documents to “Asymptotic flag of an orientable measured foliation”

Extending the Dehn quandle to shears and foliations on the torus

Reza Chamanara, Jun Hu, Joel Zablow (2014)

Fundamenta Mathematicae

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The Dehn quandle, Q, of a surface was defined via the action of Dehn twists about circles on the surface upon other circles. On the torus, 𝕋², we generalize this to show the existence of a quandle Q̂ extending Q and whose elements are measured geodesic foliations. The quandle action in Q̂ is given by applying a shear along such a foliation to another foliation. We extend some results which related Dehn quandle homology to the monodromy of Lefschetz fibrations. We apply certain quandle...

The Poincaré-Bendixson theorem and arational foliations on the sphere

Igor Nikolaev (1996)

Annales de l'institut Fourier

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Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.

Tischler fibrations of open foliated sets

John Cantwell, Lawrence Conlon (1981)

Annales de l'institut Fourier

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Let M be a closed, foliated manifold, and let U be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which U admits an approximating (Tischler) fibration over S 1 . If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.