Heegaard genus and complexity of fibered knots

Pub Date : 2022-11-08 DOI:10.1112/topo.12268

Mustafa Cengiz

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Abstract

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.

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有纤维结的精梳属和复杂性

我们证明了在三流形M$ M$中，如果一个格值大于1的纤维结K$ K$有一个足够复杂的一元，那么K$ K$就会引出一个最小格值heegard分裂P$ P$，该分裂P$ P$在同位素上是唯一的。M$ M$的小属heegard分裂是P$ P$的稳定化。我们给出了M$ M$的Heegaard格的复杂度界。我们还提供了三球面和透镜空间中纤维结的全局复杂性界限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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