Essential laminations in surgered 3-manifolds

Wu, Ying Qing

doi:10.1090/S0002-9939-1992-1104405-0

Essential laminations in surgered $3$-manifolds
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by Ying Qing Wu

Proc. Amer. Math. Soc. 115 (1992), 245-249

DOI: https://doi.org/10.1090/S0002-9939-1992-1104405-0

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Abstract:

In generic cases, an essential lamination in the interior of a $3$-manifold will remain essential after most of the Dehn fillings along a torus boundary component.

References

Marc Culler, C. McA. Gordon, J. Luecke, and Peter B. Shalen, Dehn surgery on knots, Ann. of Math. (2) 125 (1987), no. 2, 237–300. MR 881270, DOI 10.2307/1971311
David Gabai, Surgery on knots in solid tori, Topology 28 (1989), no. 1, 1–6. MR 991095, DOI 10.1016/0040-9383(89)90028-1
David Gabai, Foliations and the topology of $3$-manifolds, J. Differential Geom. 18 (1983), no. 3, 445–503. MR 723813
David Gabai and Ulrich Oertel, Essential laminations in $3$-manifolds, Ann. of Math. (2) 130 (1989), no. 1, 41–73. MR 1005607, DOI 10.2307/1971476
C. McA. Gordon, Dehn surgery and satellite knots, Trans. Amer. Math. Soc. 275 (1983), no. 2, 687–708. MR 682725, DOI 10.1090/S0002-9947-1983-0682725-0
C. McA. Gordon and R. A. Litherland, Incompressible planar surfaces in $3$-manifolds, Topology Appl. 18 (1984), no. 2-3, 121–144. MR 769286, DOI 10.1016/0166-8641(84)90005-1

Essential laminations and Dehn filling

Martin Scharlemann, Producing reducible $3$-manifolds by surgery on a knot, Topology 29 (1990), no. 4, 481–500. MR 1071370, DOI 10.1016/0040-9383(90)90017-E
Ying Qing Wu, Incompressibility of surfaces in surgered $3$-manifolds, Topology 31 (1992), no. 2, 271–279. MR 1167169, DOI 10.1016/0040-9383(92)90020-I

On the reducibility of surgered

-manifolds