Interpolation theory, loop groups and instantons.
-Kohomologie und approximationen des Laplaceoperators
Les automorphismes analytiques isométriques d'une variété complexe normée
Manifolds of smooth maps, II : the Lie group of diffeomorphisms of a non-compact smooth manifold
Manifolds of smooth maps IV : theorem of De Rham
On a diffeological group realization of certain generalized symmetrizable Kac-Moody Lie algebras.
On groups of smooth maps into a simple compact Lie group.
On infinite-dimensional grassmannians and their quantum deformations
On the transverse Scalar Curvature of a Compact Sasaki Manifold
We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in Kähler geometry described by S.K. Donaldson [10, 11], which involves the geometry of infinitedimensional groups and spaces, can be applied to the constant scalar curvature metrics in Sasaki geometry with only few modification. We prove that the space of Sasaki metrics is an infinite dimensional symmetric space and that the transverse scalar curvature of a Sasaki metric is a moment map of the...
Ordinary differential equations on infinite dimensional manifolds.
Projective limits of Banach vector bundles.
Regular infinite dimensional Lie groups.
Régularité des solutions d'équations aux dérivées partielles non linéaires associées à un système de champs de vecteurs
Cet article considère des équations aux dérivées partielles non linéaires de la forme , , où les sont des champs de vecteur vérifiant la condition de Hörmander. Soit une solution réelle de classe ; on suppose que la localisation de l’opérateur linéarisé sur le groupe de Lie associé au système est hypoelliptique; nous démontrons sous ces hypothèses que est de classe .
Relative Inversion in der Störungstheorie von Operatoren und ...-Algebren.
Remarks on the cohomological classification of certain Fréchet bundles.
Representation of a gauge group as motions of a Hilbert space
This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject.In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered as a Lie group. The second...
Spinorial matter and general relativity theory
Splitting theorems for the double tangent bundles of Fréchet manifolds.
Strongly differentiable monoids with smooth boundary.
The diffeomorphism group of a Lie foliation
We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus , . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for , P. Iglesias and...