Taut foliations of 3-manifolds and suspensions of S 1
Annales de l'Institut Fourier, Volume 42 (1992) no. 1-2, p. 193-208

Let M be a compact oriented 3-manifold whose boundary contains a single torus P and let be a taut foliation on M whose restriction to 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.

Soit M une variété compacte orientée dont le bord contient un seul tore P et soit un feuilletage taut (i.e. dont toute feuille coupe une transversale fermée) sur M dont la restriction à 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.

@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},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {42},
     number = {1-2},
     year = {1992},
     pages = {193-208},
     doi = {10.5802/aif.1289},
     zbl = {0736.57010},
     mrnumber = {93d:57028},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1992__42_1-2_193_0}
}
Taut foliations of 3-manifolds and suspensions of $S^1$. Annales de l'Institut Fourier, Volume 42 (1992) no. 1-2, pp. 193-208. doi : 10.5802/aif.1289. http://www.numdam.org/item/AIF_1992__42_1-2_193_0/

[B] J. Berge, The knots in D2 - S1 which have non trivial surgeries yielding D2 - S1, Top. and App., to appear.

[Br] M. Brittenham, Essential laminations in Seifert fibered spaces, preprint. | Zbl 0791.57013

[D] A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. de Math., 11 (1932). | JFM 58.1124.04

[F] S.R. Fenley, Quasi-Fuchsian Seifert surfaces, preprint. | Zbl 0902.57003

[FS] R. Fintushel & R. Stern, Constructing lens spaces from surgery on knots, Math. Zeitschrift, 175 (1980), 33-51. | MR 82i:57009a | Zbl 0425.57001

[GK] D. Gabai & W.H. Kazez, Pseudo-Anosov maps and surgery on fibred 2-bridge knots, Top. and App., 37 (1990), 93-100. | MR 91j:57005 | Zbl 0714.57004

[GM] D. Gabai & L. Mosher, Laminations and pseudo-Anosov flows transverse to finite depth foliations, in prep.

[GO] D. Gabai & U. Oertel, Essential laminations in 3-manifolds, Ann. Math., 130 (1989), 41-73. | MR 90h:57012 | Zbl 0685.57007

[Ha] A. Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa, 3 (1962), 367-397. | Numdam | MR 32 #6487 | Zbl 0122.40702

[HO] A. Hatcher & U. Oertel, Personal communication.

[M] W.P. Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology, 23 (1984), 225-246. | MR 86b:57004 | Zbl 0525.57003

[N] S.P. Novikov, Topology of foliations, Trans. Mos. Math. Soc., 14 (1963), 268-305. | MR 34 #824 | Zbl 0247.57006

[R] R. Rousserie, Plongements dans les variétés feuilletées et classification de feuilletages sans holonomie, IHES, 43 (1973), 101-142. | Numdam | Zbl 0356.57017

[Ro] H. Rosenberg, Foliations by planes, Topology, 6 (1967), 131-138. | Zbl 0157.30504

[Sc] M. Scharlemann, Producing reducible manifolds by surgery on a knot, Topology, 29 (1990), 481-500. | MR 91i:57003 | Zbl 0727.57015

[T] W.P. Thurston, A norm for the homology of 3-manifolds, Memoirs AMS, 339 (1986), 99-139. | MR 88h:57014 | Zbl 0585.57006

[Ti] S. Tischler, Totally parallelizable 3-manifolds, Topological dynamics, Auslander and Gottshalk eds. Benjamin (1968), 471-492. | MR 38 #3884 | Zbl 0201.56501

[W] Y. Wu, Essential laminations in surgered manifolds, preprint. | Zbl 0746.57006