Abstract
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 S L ˜ ( 2 , R ) foliation on a closed 5-manifold whose leaf is diffeomorphic to a 2-sphere minus a Cantor set.
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