{"title":"CONNECTEDNESS OF THE CUT SYSTEM COMPLEX ON NONORIENTABLE SURFACES","authors":"Fatema Ali, F. Atalan","doi":"10.46793/kgjmat2201.021a","DOIUrl":null,"url":null,"abstract":"Let N be a compact, connected, nonorientable surface of genus g with n boundary components. In this note, we show that the cut system complex of N is connected for g < 4 and disconnected for g ≥ 4. We then define a related complex and show that it is connected for g ≥ 4.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kragujevac Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46793/kgjmat2201.021a","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let N be a compact, connected, nonorientable surface of genus g with n boundary components. In this note, we show that the cut system complex of N is connected for g < 4 and disconnected for g ≥ 4. We then define a related complex and show that it is connected for g ≥ 4.
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