Let be a closed, foliated manifold, and let be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which admits an approximating (Tischler) fibration over . 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.
Soit une variété feuilletée, 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 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.
@article{AIF_1981__31_2_113_0, author = {Cantwell, John and Conlon, Lawrence}, title = {Tischler fibrations of open foliated sets}, journal = {Annales de l'Institut Fourier}, pages = {113--135}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {31}, number = {2}, year = {1981}, doi = {10.5802/aif.831}, zbl = {0442.57007}, mrnumber = {83e:57021}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.831/} }
TY - JOUR AU - Cantwell, John AU - Conlon, Lawrence TI - Tischler fibrations of open foliated sets JO - Annales de l'Institut Fourier PY - 1981 SP - 113 EP - 135 VL - 31 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.831/ DO - 10.5802/aif.831 LA - en ID - AIF_1981__31_2_113_0 ER -
%0 Journal Article %A Cantwell, John %A Conlon, Lawrence %T Tischler fibrations of open foliated sets %J Annales de l'Institut Fourier %D 1981 %P 113-135 %V 31 %N 2 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.831/ %R 10.5802/aif.831 %G en %F AIF_1981__31_2_113_0
Cantwell, John; Conlon, Lawrence. Tischler fibrations of open foliated sets. Annales de l'Institut Fourier, Volume 31 (1981) no. 2, pp. 113-135. doi : 10.5802/aif.831. https://aif.centre-mersenne.org/articles/10.5802/aif.831/
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