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P L representations of Anosov foliations

N. Hashiguchi (1992)

Annales de l'institut Fourier

By choosing certain Birkhoff’s section to the geodesic flow of a negatively curved closed surface, E. Ghys showed that the unstable foliation of the geodesic flow has a transversely piecewise linear structure. We explicitly describe the holonomy homomorphism induced by this transversely piecewise linear structure and calculate its discrete Godbillon-Vey invariant.

Parametrized h -cobordism theory

Allen E. Hatcher (1973)

Annales de l'institut Fourier

This paper gives an expository account of the author’s work on the “second” obstruction to deforming a pseudo-isotopy on a smooth compact manifold to an isotopy. Using earlier results on the “first” obstruction, due independently to J.B. Wagoner and the author, this completes the generalization of J. Cerf’s pseudo-isotopy theorem to the non-simply-connected case.

Persistance des sous-variétés à bord et à coins normalement dilatées

Pierre Berger (2011)

Annales de l’institut Fourier

On se propose de montrer que les variétés à bord et plus généralement à coins, normalement dilatées par un endomorphisme sont persistantes en tant que stratifications a -régulières. Ce résultat sera démontré en classe C s , pour s 1 . On donne aussi un exemple simple d’une sous-variété à bord normalement dilatée mais qui n’est pas persistante en tant que sous-variété différentiable.

Perturbations of the metric in Seiberg-Witten equations

Luca Scala (2011)

Annales de l’institut Fourier

Let M a compact connected oriented 4-manifold. We study the space Ξ of Spin c -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on M . In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all Spin c -structures  Ξ . We prove that, on a complex Kähler surface, for an hermitian metric h sufficiently close to the original Kähler metric, the moduli space...

Pierrot's theorem for singular Riemannian foliations.

Robert A. Wolak (1994)

Publicacions Matemàtiques

Let F be a singular Riemannian foliation on a compact connected Riemannian manifold M. We demonstrate that global foliated vector fields generate a distribution tangent to the strata defined by the closures of leaves of F and which, in each stratum, is transverse to these closures of leaves.

Planar vector field versions of Carathéodory's and Loewner's conjectures.

Carlos Gutiérrez, Federico Sánchez Bringas (1997)

Publicacions Matemàtiques

Let r = 3, 4, ... , ∞, ω. The Cr-Carathéodory's Conjecture states that every Cr convex embedding of a 2-sphere into R3 must have at least two umbilics. The Cr-Loewner's conjecture (stronger than the one of Carathéodory) states that there are no umbilics of index bigger than one. We show that these two conjectures are equivalent to others about planar vector fields. For instance, if r ≠ ω, Cr-Carathéodory's Conjecture is equivalent to the following one:Let ρ > 0 and β: U ⊂ R2 → R, be of class...

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