We prove that if a fibered knot $K$ with genus greater than 1 in a three-manifold $M$ has a sufficiently complicated monodromy, then $K$ induces a minimal genus Heegaard splitting $P$ that is unique up to isotopy, and small genus Heegaard splittings of $M$ are stabilizations of $P$. We provide a complexity bound in terms of the Heegaard genus of $M$. We also provide global complexity bounds for fibered knots in the three-sphere and lens spaces.

中文翻译：

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Heegaard 属和纤维结的复杂性

我们证明，如果一个纤维结$ķ$在三流形中具有大于 1 的属$米$有一个足够复杂的单态，那么$ķ$诱导最小属 Heegaard 分裂$磷$这是唯一的同位素，和小属 Heegaard 分裂$米$是稳定的$磷$. 我们提供了根据 Heegaard 属的复杂性界限$米$. 我们还为三球和透镜空间中的纤维结提供全局复杂性界限。