Ends of leaves of Lie foliations

DOI Web Site 参考文献31件
  • HECTOR Gilbert
    Institute de Mathématique et Informatiques Université Claude Bernard-Lyon I
  • MATSUMOTO Shigenori
    Department of Mathematics College of Science and Technology Nihon University
  • MEIGNIEZ Gaël
    Laboratoire de mathematiques et applications des mathematiques Universite de Bretagne Sud

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Let G be a simply connected Lie group and consider a Lie G foliation \mathscr F on a closed manifold M whose leaves are all dense in M. Then the space of ends {\mathscr E}(F) of a leaf F of \mathscr 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 \mathscr Fadmits a transverse Riemannian foliation of the complementary dimension, then {\mathscr E}(F) consists of one or two points. On the contrary there exists a Lie \widetilde{SL}(2, \bm{R}) foliation on a closed 5-manifold whose leaf is diffeomorphic to a 2-sphere minus a Cantor set.

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