Taut foliations of 3-manifolds and suspensions of $S^1$

Gabai, David

doi:10.5802/aif.1289

Taut foliations of 3-manifolds and suspensions of

S^{1}

Gabai, David

Annales de l'Institut Fourier, …, Tome 42 (1992) no. 1-2, pp. 193-208.

Résumé
Abstract

Soit $M$ une variété compacte orientée dont le bord contient un seul tore $P$ et soit $ℱ$ un feuilletage taut (i.e. dont toute feuille coupe une transversale fermée) sur $M$ dont la restriction à $\partial M$ a une composante de Reeb. Le principal résultat technique de ce papier dit que si $N$ est obtenue par chirurgie de Dehn sur $P$ le long de toute courbe parallèle à la composante de Reeb, alors $N$ admet un feuilletage taut.

Let $M$ be a compact oriented 3-manifold whose boundary contains a single torus $P$ and let $ℱ$ be a taut foliation on $M$ whose restriction to $\partial M$ has a Reeb component. The main technical result of the paper, asserts that if $N$ is obtained by Dehn filling $P$ along any curve not parallel to the Reeb component, then $N$ has a taut foliation.

MR Zbl

DOI : 10.5802/aif.1289

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     author = {Gabai, David},
     title = {Taut foliations of 3-manifolds and suspensions of $S^1$},
     journal = {Annales de l'Institut Fourier},
     pages = {193--208},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {42},
     number = {1-2},
     year = {1992},
     doi = {10.5802/aif.1289},
     mrnumber = {93d:57028},
     zbl = {0736.57010},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1289/}
}

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Gabai, David. Taut foliations of 3-manifolds and suspensions of $S^1$. Annales de l'Institut Fourier, …, Tome 42 (1992) no. 1-2, pp. 193-208. doi : 10.5802/aif.1289. http://www.numdam.org/articles/10.5802/aif.1289/

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