For a compact, orientable, irreducible 3-manifold with toroidal boundary that is not the product of a torus and an interval or a cable space, each boundary torus has a finite set of slopes such that, if avoided, the Thurston norm of a Dehn filling behaves predictably. More precisely, for all but finitely many slopes, the Thurston norm of a class in the second homology of the filled manifold plus the so-called winding norm of the class will be equal to the Thurston norm of the corresponding class in the second homology of the unfilled manifold. This generalizes a result of Sela and is used to answer a question of Baker-Motegi concerning the Seifert genus of knots obtained by twisting a given initial knot along an unknot which links it.

中文翻译：

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Dehn 填充和 Thurston 范数

对于具有环形边界的紧凑、可定向、不可约 3 流形，它不是环面和区间或索空间的乘积，每个边界环面都有一组有限的斜率，如果避免，则为 Dehn 的 Thurston 范数填充行为可预测。更准确地说，对于除有限多个斜率之外的所有斜率，填充流形的第二个同调中的类的 Thurston 范数加上该类的所谓缠绕范数将等于对应类的第二个同调中的 Thurston 范数未填充的歧管。这概括了 Sela 的结果，并用于回答 Baker-Motegi 提出的关于结的 Seifert 属的问题，该结是通过将给定的初始结沿着连接它的不结点扭转而获得的。