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Foliations of surfaces I : an ideal boundary

John N. Mather — 1982

Annales de l'institut Fourier

Let F be a foliation of the punctured plane P . Any non-compact leaf of F has two ends, which we call leaf-ends. The set of leaf-ends which converge to the origin has a natural cyclic order. In the case is infinite, we show that the cyclicly ordered set β , obtained by identifying neighbors in and filling in the holes according to the Dedeking process, is equivalent to a circle. We show that the set P β has a natural topology, and it is homeomorphic to S 1 × [ 0 , ) with respect to this topology.

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