We prove that any mapping torus of a pseudo-Anosov mapping class with bounded normalized Weil-Petersson translation length contains a finite set of transverse and level closed curves, and drilling out this set of curves results in one of a finite number of cusped hyperbolic 3-manifolds. The number of manifolds in the finite list depends only on the bound for normalized translation length. We also prove a complementary result that explains the necessity of removing level curves by producing new estimates for the Weil-Petersson translation length of compositions of pseudo-Anosov mapping classes and arbitrary powers of a Dehn twist.

中文翻译：

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Weil-Petersson 平移长度和具有许多纤维填充物的流形

我们证明了具有有界归一化 Weil-Petersson 平移长度的伪 Anosov 映射类的任何映射环包含一组有限的横向和水平闭合曲线，并且钻出这组曲线会导致有限数量的有尖双曲线 3 中的一个-歧管。有限列表中的流形数量仅取决于归一化平移长度的界限。我们还证明了一个补充结果，该结果通过对伪 Anosov 映射类和 Dehn 扭曲的任意幂的组合的 Weil-Petersson 平移长度产生新的估计来解释去除水平曲线的必要性。