Ends of leaves of Lie foliations

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概要

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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.

• 社団法人 日本数学会の論文
• 2005-07-01

著者

• MATSUMOTO Shigenori

  Department of Mathematics College of Science and Technology Nihon University

• Matsumoto Shigenori

  Department Of Applied Physics School Of Engineering The University Of Tokyo

• HECTOR Gilbert

  Institute de Mathematique et Informatiques Universite Claude Bernard-Lyon I

• MEIGNIEZ Gael

  Laboratoire de mathematiques et applications des mathematiques Universite de Bretagne Sud

• Hector Gilbert

  Institut C. Jordan Umr Cnrs 5028 Universite C. Bernard (lyon 1)

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