{"title":"Seifert链的循环分支盖及与ADE$ ADE$链猜想有关的性质","authors":"Steven Boyer, Cameron McA. Gordon, Ying Hu","doi":"10.1112/jlms.70178","DOIUrl":null,"url":null,"abstract":"<p>In this article, we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not <span></span><math>\n <semantics>\n <mi>L</mi>\n <annotation>$L$</annotation>\n </semantics></math>-spaces, if and only if it is not an <span></span><math>\n <semantics>\n <mrow>\n <mi>A</mi>\n <mi>D</mi>\n <mi>E</mi>\n </mrow>\n <annotation>$ADE$</annotation>\n </semantics></math> link up to orientation. This leads to a proof of the <span></span><math>\n <semantics>\n <mrow>\n <mi>A</mi>\n <mi>D</mi>\n <mi>E</mi>\n </mrow>\n <annotation>$ADE$</annotation>\n </semantics></math> link conjecture for Seifert links. When <span></span><math>\n <semantics>\n <mi>L</mi>\n <annotation>$L$</annotation>\n </semantics></math> is an <span></span><math>\n <semantics>\n <mrow>\n <mi>A</mi>\n <mi>D</mi>\n <mi>E</mi>\n </mrow>\n <annotation>$ADE$</annotation>\n </semantics></math> link up to orientation, we determine which of its canonical <span></span><math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math>-fold cyclic branched covers <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>Σ</mi>\n <mi>n</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>L</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\Sigma _n(L)$</annotation>\n </semantics></math> have nonleft-orderable fundamental groups. In addition, we give a topological proof of Ishikawa's classification of strongly quasi-positive Seifert links and we determine the Seifert links that are definite, resp., have genus zero, resp. have genus equal to its smooth 4-ball genus, among others. In the last section, we provide a comprehensive survey of the current knowledge and results concerning the <span></span><math>\n <semantics>\n <mrow>\n <mi>A</mi>\n <mi>D</mi>\n <mi>E</mi>\n </mrow>\n <annotation>$ADE$</annotation>\n </semantics></math> link conjecture.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 6","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70178","citationCount":"0","resultStr":"{\"title\":\"Cyclic branched covers of Seifert links and properties related to the \\n \\n \\n A\\n D\\n E\\n \\n $ADE$\\n link conjecture\",\"authors\":\"Steven Boyer, Cameron McA. Gordon, Ying Hu\",\"doi\":\"10.1112/jlms.70178\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not <span></span><math>\\n <semantics>\\n <mi>L</mi>\\n <annotation>$L$</annotation>\\n </semantics></math>-spaces, if and only if it is not an <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>A</mi>\\n <mi>D</mi>\\n <mi>E</mi>\\n </mrow>\\n <annotation>$ADE$</annotation>\\n </semantics></math> link up to orientation. This leads to a proof of the <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>A</mi>\\n <mi>D</mi>\\n <mi>E</mi>\\n </mrow>\\n <annotation>$ADE$</annotation>\\n </semantics></math> link conjecture for Seifert links. When <span></span><math>\\n <semantics>\\n <mi>L</mi>\\n <annotation>$L$</annotation>\\n </semantics></math> is an <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>A</mi>\\n <mi>D</mi>\\n <mi>E</mi>\\n </mrow>\\n <annotation>$ADE$</annotation>\\n </semantics></math> link up to orientation, we determine which of its canonical <span></span><math>\\n <semantics>\\n <mi>n</mi>\\n <annotation>$n$</annotation>\\n </semantics></math>-fold cyclic branched covers <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>Σ</mi>\\n <mi>n</mi>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>L</mi>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$\\\\Sigma _n(L)$</annotation>\\n </semantics></math> have nonleft-orderable fundamental groups. In addition, we give a topological proof of Ishikawa's classification of strongly quasi-positive Seifert links and we determine the Seifert links that are definite, resp., have genus zero, resp. have genus equal to its smooth 4-ball genus, among others. In the last section, we provide a comprehensive survey of the current knowledge and results concerning the <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>A</mi>\\n <mi>D</mi>\\n <mi>E</mi>\\n </mrow>\\n <annotation>$ADE$</annotation>\\n </semantics></math> link conjecture.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"111 6\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70178\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70178\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70178","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在这篇文章中，我们证明了一个Seifert环的所有循环分支覆盖都有左序基群，因此承认共取向紧叶，并且不是L$ L$ -空间，当且仅当它不是一个指向方向的a DE$ ADE$环。这导致了对Seifert链接的a DE$ ADE$链接猜想的证明。当L$ L$是指向方向的A $ D $ E$ ADE$时，我们确定了它的正则n$ n$ -fold循环分支覆盖Σ n(L)$ \Sigma _n(L)$具有非左序基本群。此外，我们给出了Ishikawa的强拟正Seifert连杆分类的拓扑证明，并确定了Seifert连杆是确定的。，属为0。具有与其光滑的4球属相等的属。在最后一节中，我们对目前关于a - D - E - ADE -链接猜想的知识和结果进行了全面的综述。
Cyclic branched covers of Seifert links and properties related to the
A
D
E
$ADE$
link conjecture
In this article, we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not -spaces, if and only if it is not an link up to orientation. This leads to a proof of the link conjecture for Seifert links. When is an link up to orientation, we determine which of its canonical -fold cyclic branched covers have nonleft-orderable fundamental groups. In addition, we give a topological proof of Ishikawa's classification of strongly quasi-positive Seifert links and we determine the Seifert links that are definite, resp., have genus zero, resp. have genus equal to its smooth 4-ball genus, among others. In the last section, we provide a comprehensive survey of the current knowledge and results concerning the link conjecture.
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
