Year: 1982
Type: article
Abstract: 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 ℰ of leaf-ends which converge to the origin has a natural cyclic order. In the case ℰ is infinite, we show that the cyclicly ordered set β , obtained by identifying neighbors in ℰ 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.
Source: Annales de l’institut Fourier
DOI: 10.5802/aif.867
Author: John N. Mather
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2323546321