{"title":"Hyperbolic surfaces with sublinearly many systoles that fill","authors":"Maxime Fortier Bourque","doi":"10.4171/cmh/495","DOIUrl":null,"url":null,"abstract":"For any e>0, we construct a closed hyperbolic surface of genus g=g(e) with a set of at most eg systoles that fill, meaning that each component of the complement of their union is contractible. This surface is also a critical point of index at most eg for the systole function, disproving the lower bound of 2g−1 conjectured by Schmutz Schaller.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2019-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/cmh/495","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Commentarii Mathematici Helvetici","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/cmh/495","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 7
Abstract
For any e>0, we construct a closed hyperbolic surface of genus g=g(e) with a set of at most eg systoles that fill, meaning that each component of the complement of their union is contractible. This surface is also a critical point of index at most eg for the systole function, disproving the lower bound of 2g−1 conjectured by Schmutz Schaller.
期刊介绍：
Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals.
Commentarii Mathematici Helvetici is covered in:
Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.
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