Tischler fibrations of open foliated sets
Annales de l'Institut Fourier, Tome 31 (1981) no. 2, pp. 113-135.

Soit M une variété feuilletée, U une partie ouverte et connexe qui est une réunion de feuilles localement dense et sans holonomie. On étudie les conditions entraînant l’existence d’une fibration (de Tischler) sur S 1 qui s’approche du feuilletage. D’autre part en posant l’existence d’une telle fibration, on considère les conditions sous lesquelles les feuilles sont des revêtements réguliers des fibres. Finalement, on discute quelques exemples montrant que nos hypothèses supplémentaires sont, en fait, requises.

Let M be a closed, foliated manifold, and let U be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which U admits an approximating (Tischler) fibration over S 1 . If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.

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     title = {Tischler fibrations of open foliated sets},
     journal = {Annales de l'Institut Fourier},
     pages = {113--135},
     publisher = {Institut Fourier},
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Cantwell, John; Conlon, Lawrence. Tischler fibrations of open foliated sets. Annales de l'Institut Fourier, Tome 31 (1981) no. 2, pp. 113-135. doi : 10.5802/aif.831. http://www.numdam.org/articles/10.5802/aif.831/

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