Frobenius avec singularités
From Banach to distributions and currents
From elementary algebra to Bäcklund transformations
Functions with prescribed singularities
The distributional -dimensional Jacobian of a map in the Sobolev space which takes values in the sphere can be viewed as the boundary of a rectifiable current of codimension carried by (part of) the singularity of which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary of codimension can be realized as Jacobian of a Sobolev map valued in . In case is polyhedral, the map we construct...
Functorial prolongations of Lie groupoids
For every Lie groupoid Φ with m-dimensional base M and every fiber product preserving bundle functor F on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps, we construct a Lie groupoid ℱ Φ over M. Every action of Φ on a fibered manifold Y → M is extended to an action of ℱ Φ on FY → M.
Functorial prolongations of Lie groups and their actions
Fundamental solutions and geometry of the sum of squares of vector fields.
Fundamental vector fields on associated fiber bundles
Fundamental vector fields on type fibres of jet prolongations of tensor bundles