Spaces of retractions which are homeomorphic to Hilbert space
Stability of Transversality to a Stratification Implies Whitney (a)-Regularity.
Strong density for higher order Sobolev spaces into compact manifolds
Given a compact manifold , an integer and an exponent , we prove that the class of smooth maps on the cube with values into is dense with respect to the strong topology in the Sobolev space when the homotopy group of order is trivial. We also prove density of maps that are smooth except for a set of dimension , without any restriction on the homotopy group of .
Sur le théorème des fonctions composées différentiables
Soit un morphisme propre relativement algébrique entre espaces semi-analytiques. On montre que si désigne l’anneau des fonctions de classe sur , l’image par de est fermée dans muni de sa topologie naturelle d’espace de Frechet ; ceci généralise un résultat précédent de J.-C. Tougeron (lui-même généralisant un résultat de Glaeser) qui traite du cas semi-algébrique. La méthode est tout à fait analogue et utilise des propriétés algébriques de l’anneau des fonctions Nash-analytiques introduit...
The closure of the space of homeomorphisms on a manifold. The piecewise linear case
The cohomology of holomorphic self maps of the Riemann sphere.
The conformal structure of Riemann surfaces with boundary parametrizing minimal surfaces.
The family of isometric superconformal harmonic maps and the affine Toda equations.
The geometry of the moduli space of CP2 instantons.
The Lie group of real analytic diffeomorphisms is not real analytic
We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense of Milnor. ...
The space : minimal connection and optimal lifting
The space of Lipschitz maps from a compactum to an absolute neighborhood LIP extensor
The symplectic geometry of affine connenctions on surfaces.
The tangent bundle of an almost-complex free loopspace.
Topologically -determined map germs are topologically cone-like
Über Stabilität und Isoliertheit der Lösungen des Klassischen Plateauproblems.
Une propriété générique des couples de champs de vecteurs
Une stratification de l'espace des structures riemanniennes
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms.
Variational calculus on Lie algebroids
It is shown that the Lagrange's equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.