Displaying similar documents to “Formal manifolds and synthetic theory of jet bundles”

Lie groupoids as generalized atlases

Jean Pradines (2004)

Open Mathematics

Similarity:

Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the “virtual structure” of its orbit space, the equivalence between atlases being here the smooth Morita equivalence. This “structure” keeps memory of the isotropy groups and of the smoothness as well. To take the smoothness into account, we claim that we can go very far by retaining just a few formal properties...

Functorial prolongations of Lie groupoids

Ivan Kolář (2007)

Banach Center Publications

Similarity:

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.