Displaying similar documents to “Basic concepts of the theory of geometric objects”

On the geometric concomitants

Zenon Moszner (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this note the necessary and sufficient conditon it would the concomitant of the geometric object was the geometric object too is given.

Lie groupoids as generalized atlases

Jean Pradines (2004)

Open Mathematics

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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...