Groups that do not act by automorphisms of codimension-one foliations

Details Groups that do not act by automorphisms of codimension-one foliations Groups that do not act by automorphisms of codimension-one foliations

2000-08-01

arxiv.org/abs/math/0008012v1

Mathematics

Geometric Topology

Latex2e file, 15 pages, no figures

Scientific paper

Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least two have this property.) Suppose that such a G 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 G fixes a compact leaf of F. Furthermore, we give sufficient conditions for some finite-index subgroup of G to fix each leaf of F.

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