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Foliations by planes and Lie group actions

J. A. Álvarez López; J. L. Arraut; C. Biasi — 2003

Annales Polonici Mathematici

Let N be a closed orientable n-manifold, n ≥ 3, and K a compact non-empty subset. We prove that the existence of a transversally orientable codimension one foliation on N∖K with leaves homeomorphic to $ℝ^{n - 1}$ , in the relative topology, implies that K must be connected. If in addition one imposes some restrictions on the homology of K, then N must be a homotopy sphere. Next we consider C² actions of a Lie group diffeomorphic to $ℝ^{n - 1}$ on N and obtain our main result: if K, the set of singular points of the...

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