{"title":"非退化曲线空间的拓扑结构","authors":"M Z Shapiro","doi":"10.1070/IM1994v043n02ABEH001565","DOIUrl":null,"url":null,"abstract":"A curve on a sphere or on a projective space is called nondegenerate if it has a nondegenerate moving frame at every point. The number of homotopy classes of closed nondegenerate curves immersed in the sphere or projective space is computed. In the case of the sphere Sn, this turns out to be 4 for odd n≥3 and 6 for even n≥2; in the case of the projective space Pn, 10 for odd n≥3 and 3 for even n≥2.","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"TOPOLOGY OF THE SPACE OF NONDEGENERATE CURVES\",\"authors\":\"M Z Shapiro\",\"doi\":\"10.1070/IM1994v043n02ABEH001565\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A curve on a sphere or on a projective space is called nondegenerate if it has a nondegenerate moving frame at every point. The number of homotopy classes of closed nondegenerate curves immersed in the sphere or projective space is computed. In the case of the sphere Sn, this turns out to be 4 for odd n≥3 and 6 for even n≥2; in the case of the projective space Pn, 10 for odd n≥3 and 3 for even n≥2.\",\"PeriodicalId\":158473,\"journal\":{\"name\":\"Russian Academy of Sciences. Izvestiya Mathematics\",\"volume\":\"46 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Academy of Sciences. Izvestiya Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1994v043n02ABEH001565\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Academy of Sciences. Izvestiya Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1994v043n02ABEH001565","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A curve on a sphere or on a projective space is called nondegenerate if it has a nondegenerate moving frame at every point. The number of homotopy classes of closed nondegenerate curves immersed in the sphere or projective space is computed. In the case of the sphere Sn, this turns out to be 4 for odd n≥3 and 6 for even n≥2; in the case of the projective space Pn, 10 for odd n≥3 and 3 for even n≥2.
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