Ends of leaves of Lie foliations
Résumé
Let G be a simply connected Lie group and consider a Lie G foliation F on a closed manifold M whose leaves are all dense in M. Then the space of ends E (F) of a leaf F of F is shown to be either a singleton, a two points set, or a Cantor set. Further if G is solvable, or if G has no cocompact discrete normal subgroup and F admits a transverse Riemannian foliation of the complementary dimension, then E (F) consists of one or two points. On the contrary there exists a Lie f SL(2, R) foliation on a closed 5-manifold whose leaf is diffeomorphic to a 2-sphere minus a Cantor set.
Domaines
Topologie géométrique [math.GT]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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