Taut foliations, positive 3-braids, and the L-space conjecture

摘要

We construct taut foliations in every closed 3-manifold obtained byr-framed Dehn surgery along a positive 3-braid knotKinS3, wherer<2g(K)-1andg(K)denotes the Seifert genus ofK. This confirms a prediction of the L-space Conjecture. For instance, we produce taut foliations in every non-L-space obtained by surgery along the pretzel knotP(-2,3,7), and indeed along every pretzel knotP(-2,3,q), forqa positive odd integer. This is the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. Additionally, we construct taut foliations in every closed 3-manifold obtained byr-framed Dehn surgery along a positive 1-bridge braid inS3, wherer