Heegaard genus and complexity of fibered knots

IF 0.8 2区数学 Q2 MATHEMATICS Journal of Topology Pub Date : 2022-11-08 DOI:10.1112/topo.12268

Mustafa Cengiz

{"title":"Heegaard genus and complexity of fibered knots","authors":"Mustafa Cengiz","doi":"10.1112/topo.12268","DOIUrl":null,"url":null,"abstract":"<p>We prove that if a fibered knot <math>\n <semantics>\n <mi>K</mi>\n <annotation>$K$</annotation>\n </semantics></math> with genus greater than 1 in a three-manifold <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> has a sufficiently complicated monodromy, then <math>\n <semantics>\n <mi>K</mi>\n <annotation>$K$</annotation>\n </semantics></math> induces a minimal genus Heegaard splitting <math>\n <semantics>\n <mi>P</mi>\n <annotation>$P$</annotation>\n </semantics></math> that is unique up to isotopy, and small genus Heegaard splittings of <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> are stabilizations of <math>\n <semantics>\n <mi>P</mi>\n <annotation>$P$</annotation>\n </semantics></math>. We provide a complexity bound in terms of the Heegaard genus of <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math>. We also provide global complexity bounds for fibered knots in the three-sphere and lens spaces.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2389-2425"},"PeriodicalIF":0.8000,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12268","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

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.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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。

求助全文

约1分钟内获得全文去求助

来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.