{"title":"Nearly fibered links with genus one","authors":"A. Cavallo, I. Matkovič","doi":"10.1007/s10474-023-01364-0","DOIUrl":null,"url":null,"abstract":"<div><p>We classify all the <span>\\(n\\)</span>-component links in the <span>\\(3\\)</span>-sphere that bound\na Thurston norm minimizing Seifert surface <span>\\(\\Sigma\\)</span> with Euler characteristic <span>\\(\\chi(\\Sigma)=n-2\\)</span> and that are nearly fibered, which means that the rank of their link Floer\nhomology group <span>\\(\\widehat{HFL}\\)</span> in the maximal (collapsed) Alexander grading <span>\\(s_{\\text{top}}\\)</span> is equal\nto two. In other words, such a link <span>\\(L\\)</span> satisfies <span>\\(s_{\\text{top}}=\\frac{n-\\chi(\\Sigma)}{2}=1\\)</span>, and in addition <span>\\({\\rm rk}\\widehat{HFL}_{*}(L)[1]=2\\)</span> and <span>\\({\\rm rk}\\widehat{HFL}_{*}(L)[s]=0\\)</span> for every <span>\\(s>1\\)</span>.</p><p>The proof of the main theorem is inspired by the one of a similar recent result for knots by Baldwin and Sivek, and involves techniques from sutured Floer\nhomology. Furthermore, we also compute the group <span>\\(\\widehat{HFL}\\)</span> for each of these links.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-023-01364-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We classify all the \(n\)-component links in the \(3\)-sphere that bound
a Thurston norm minimizing Seifert surface \(\Sigma\) with Euler characteristic \(\chi(\Sigma)=n-2\) and that are nearly fibered, which means that the rank of their link Floer
homology group \(\widehat{HFL}\) in the maximal (collapsed) Alexander grading \(s_{\text{top}}\) is equal
to two. In other words, such a link \(L\) satisfies \(s_{\text{top}}=\frac{n-\chi(\Sigma)}{2}=1\), and in addition \({\rm rk}\widehat{HFL}_{*}(L)[1]=2\) and \({\rm rk}\widehat{HFL}_{*}(L)[s]=0\) for every \(s>1\).
The proof of the main theorem is inspired by the one of a similar recent result for knots by Baldwin and Sivek, and involves techniques from sutured Floer
homology. Furthermore, we also compute the group \(\widehat{HFL}\) for each of these links.
期刊介绍:
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.