Mathematics – Differential Geometry
Scientific paper
2007-11-13
CEJM 2(5) 2004 624-662
Mathematics
Differential Geometry
34 pages, lecture delivered at the 5th Conference on Geometry ans Topology of Manifolds, Krynica (Poland), April 2003
Scientific paper
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.
No associations
LandOfFree
Lie Groupoids as generalized atlases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lie Groupoids as generalized atlases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lie Groupoids as generalized atlases will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-529855