Taut foliations in knot complements

Abstract

We show that for any nontrivial knot in $S^3$, there is an open interval containing zero such that a Dehn surgery on any slope in this interval yields a 3-manifold with taut foliations. This generalizes a theorem of Gabai on zero frame surgery.

19 pages, 6 figures. Minor changes; applications were added in the introduction section