# Lie groupoids as generalized atlases

Open Mathematics (2004)

- Volume: 2, Issue: 5, page 624-662
- ISSN: 2391-5455

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topJean Pradines. "Lie groupoids as generalized atlases." Open Mathematics 2.5 (2004): 624-662. <http://eudml.org/doc/268797>.

@article{JeanPradines2004,

abstract = {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 of embeddings and surmersions, yielding a very polymorphous unifying theory. We suggest further developments.},

author = {Jean Pradines},

journal = {Open Mathematics},

keywords = {58H05},

language = {eng},

number = {5},

pages = {624-662},

title = {Lie groupoids as generalized atlases},

url = {http://eudml.org/doc/268797},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Jean Pradines

TI - Lie groupoids as generalized atlases

JO - Open Mathematics

PY - 2004

VL - 2

IS - 5

SP - 624

EP - 662

AB - 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 of embeddings and surmersions, yielding a very polymorphous unifying theory. We suggest further developments.

LA - eng

KW - 58H05

UR - http://eudml.org/doc/268797

ER -

## References

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