{"title":"最小翘曲度2的初始交替结","authors":"Ayaka Shimizu","doi":"10.1142/s0218216520500601","DOIUrl":null,"url":null,"abstract":"The warping degree of an oriented knot diagram is the minimal number of crossing changes which are required to obtain a monotone knot diagram from the diagram. The minimal warping degree of a knot is the minimal value of the warping degree for all oriented minimal diagrams of the knot. In this paper, all prime alternating knots with minimal warping degree two are determined.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"69 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Prime alternating knots of minimal warping degree two\",\"authors\":\"Ayaka Shimizu\",\"doi\":\"10.1142/s0218216520500601\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The warping degree of an oriented knot diagram is the minimal number of crossing changes which are required to obtain a monotone knot diagram from the diagram. The minimal warping degree of a knot is the minimal value of the warping degree for all oriented minimal diagrams of the knot. In this paper, all prime alternating knots with minimal warping degree two are determined.\",\"PeriodicalId\":8454,\"journal\":{\"name\":\"arXiv: Geometric Topology\",\"volume\":\"69 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218216520500601\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218216520500601","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Prime alternating knots of minimal warping degree two
The warping degree of an oriented knot diagram is the minimal number of crossing changes which are required to obtain a monotone knot diagram from the diagram. The minimal warping degree of a knot is the minimal value of the warping degree for all oriented minimal diagrams of the knot. In this paper, all prime alternating knots with minimal warping degree two are determined.
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