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Foliations by planes and Lie group actions

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López J., Arraut J., Biasi C.

Annales Polonici Mathematici

2003

tom 82

nr 1

61-69

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 action, is a finite non-empty subset, then K contains only one point and N is homeomorphic to Sⁿ.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Arraut J.

1 Biasi C.

1 López J.

1 2003

Wyniki wyszukiwania

Foliations by planes and Lie group actions