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

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 ∂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 ∂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.

@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},
     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://archive.numdam.org/articles/10.5802/aif.1289/}
}
TY  - JOUR
AU  - Gabai, David
TI  - Taut foliations of 3-manifolds and suspensions of $S^1$
JO  - Annales de l'Institut Fourier
PY  - 1992
SP  - 193
EP  - 208
VL  - 42
IS  - 1-2
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.1289/
DO  - 10.5802/aif.1289
LA  - en
ID  - AIF_1992__42_1-2_193_0
ER  - 
%0 Journal Article
%A Gabai, David
%T Taut foliations of 3-manifolds and suspensions of $S^1$
%J Annales de l'Institut Fourier
%D 1992
%P 193-208
%V 42
%N 1-2
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.1289/
%R 10.5802/aif.1289
%G en
%F 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) no. 1-2, pp. 193-208. doi : 10.5802/aif.1289. http://archive.numdam.org/articles/10.5802/aif.1289/

[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

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

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

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

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

[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 | Zbl

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

[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 | Zbl

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

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

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

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

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

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

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

Cité par Sources :