Topological Equivalence of Foliations of Homogeneous Spaces
نویسنده
چکیده
For i = 1,2, let r j be a lattice in a connected Lie group G j , and let X j be a connected Lie subgroup of Gj . The double cosets rjg X j provide a foliation .9'; of the homogeneous space rj\Gj . Assume that XI and X2 are unimodular and that .91 has a dense leaf. If G I and G2 are semisimple groups to which the Mostow Rigidity Theorem applies, or are simply connected nilpotent groups (or are certain more general solvable groups), we use an idea of D. Benardete to show that any topological equivalence of .91 and .9i must be the composition of two very elementary maps: an affine map and a map that takes each leaf to itself.
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