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Des espaces homogènes à la résolution de Koszul

André Haefliger (1987)

Annales de l'institut Fourier

Cette note évoque les premiers travaux de J.-L. Koszul (1947-1950) en les replaçant dans leur cadre historique et retrace en particulier le chemin qui a conduit Koszul à la résolution qui porte son nom.

Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

Denise Halverson, Dušan Repovš (2013)

Open Mathematics

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk...

Diastolic and isoperimetric inequalities on surfaces

Florent Balacheff, Stéphane Sabourau (2010)

Annales scientifiques de l'École Normale Supérieure

We prove a universal inequality between the diastole, defined using a minimax process on the one-cycle space, and the area of closed Riemannian surfaces. Roughly speaking, we show that any closed Riemannian surface can be swept out by a family of multi-loops whose lengths are bounded in terms of the area of the surface. This diastolic inequality, which relies on an upper bound on Cheeger’s constant, yields an effective process to find short closed geodesics on the two-sphere, for instance. We deduce...

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