We construct taut foliations in every closed 3‐manifold obtained by $r$‐framed Dehn surgery along a positive 3‐braid knot $K$ in $S^3$, where $r<2g(K)-1$ and $g(K)$ denotes the Seifert genus of $K$. 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 knot $P(-2,3,7)$, and indeed along every pretzel knot $P(-2,3,q)$, for $q$ a 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 by $r$‐framed Dehn surgery along a positive 1‐bridge braid in $S^3$, where $r<g(K)$.

中文翻译：

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绷紧的叶面，正3辫子和L空间猜想

我们在由 $\mathrm{[R}$构架的Dehn手术沿3辫子结阳性 $ķ$ 在 ${\mathrm{小号}}^3$，在哪里 $\mathrm{[R}<2G（ķ）-\mathrm{1个}$ 和 $G（ķ）$ 表示的Seifert属 $ķ$。这证实了对L空间猜想的预测。例如，我们通过椒盐脆饼结在手术中获得的每个非L空间中产生张紧的叶面$P（-2，3，7）$，而且确实沿着每个椒盐脆饼结 $P（-2，3，q）$，对于 $q$正整数。这是沿无限双曲L空间结族通过手术获得的每个非L空间的拉紧叶面构造的第一个。此外，我们在由$\mathrm{[R}$沿着正1桥编织物进行框架Dehn手术 ${\mathrm{小号}}^3$，在哪里 $\mathrm{[R}<G（ķ）$。