{"title":"非定向曲面上割系统复合体的连通性","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":"{\"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}","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}
CONNECTEDNESS OF THE CUT SYSTEM COMPLEX ON NONORIENTABLE SURFACES
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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