Soit une variété compacte orientée dont le bord contient un seul tore et soit un feuilletage taut (i.e. dont toute feuille coupe une transversale fermée) sur dont la restriction à a une composante de Reeb. Le principal résultat technique de ce papier dit que si est obtenue par chirurgie de Dehn sur le long de toute courbe parallèle à la composante de Reeb, alors admet un feuilletage taut.
Let be a compact oriented 3-manifold whose boundary contains a single torus and let be a taut foliation on whose restriction to has a Reeb component. The main technical result of the paper, asserts that if is obtained by Dehn filling along any curve not parallel to the Reeb component, then has a taut foliation.
@article{AIF_1992__42_1-2_193_0, author = {Gabai, David}, title = {Taut foliations of 3-manifolds and suspensions of $S^1$}, journal = {Annales de l'Institut Fourier}, volume = {42}, year = {1992}, pages = {193-208}, doi = {10.5802/aif.1289}, mrnumber = {93d:57028}, zbl = {0736.57010}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1992__42_1-2_193_0} }
Gabai, David. Taut foliations of 3-manifolds and suspensions of $S^1$. Annales de l'Institut Fourier, Tome 42 (1992) pp. 193-208. doi : 10.5802/aif.1289. http://gdmltest.u-ga.fr/item/AIF_1992__42_1-2_193_0/
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