Abstract

Let Γ be a finitely generated group having the property that any action of any finite-index subgroup of Γ by homeomorphisms of the circle must have a finite orbit. (By a theorem of É. Ghys, lattices in simple Lie groups of real rank at least 2 have this property.) Suppose that such a Γ acts on a compact manifold M by automorphisms of a codimension-one C² foliation, F. We show that if F has a compact leaf, then some finite-index subgroup of Γ fixes a compact leaf of F. Furthermore, we give suficient conditions for some finite-index subgroup of Γ to fix each leaf of F.

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