{"title":"连杆的本征对称群","authors":"C. Livingston","doi":"10.2140/agt.2023.23.2347","DOIUrl":null,"url":null,"abstract":"The set of isotopy classes of ordered n-component links in the 3-sphere is acted on by the symmetric group via permutation of the components. The intrinsic symmetry group of the link, S(L), is defined to be the set of elements in the symmetric group that preserve the ordered isotopy type of L as an unoriented link. The study of these groups was initiated in 1969, but the question of whether or not every subgroup of the symmetric group arises as an intrinisic symmetry group of some link has remained open. We provide counterexamples; in particular, if n>5, then there does not exist an n-component link L for which S(L) is the alternating group.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"10 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Intrinsic symmetry groups of links\",\"authors\":\"C. Livingston\",\"doi\":\"10.2140/agt.2023.23.2347\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The set of isotopy classes of ordered n-component links in the 3-sphere is acted on by the symmetric group via permutation of the components. The intrinsic symmetry group of the link, S(L), is defined to be the set of elements in the symmetric group that preserve the ordered isotopy type of L as an unoriented link. The study of these groups was initiated in 1969, but the question of whether or not every subgroup of the symmetric group arises as an intrinisic symmetry group of some link has remained open. We provide counterexamples; in particular, if n>5, then there does not exist an n-component link L for which S(L) is the alternating group.\",\"PeriodicalId\":50826,\"journal\":{\"name\":\"Algebraic and Geometric Topology\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic and Geometric Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2023.23.2347\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.2347","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The set of isotopy classes of ordered n-component links in the 3-sphere is acted on by the symmetric group via permutation of the components. The intrinsic symmetry group of the link, S(L), is defined to be the set of elements in the symmetric group that preserve the ordered isotopy type of L as an unoriented link. The study of these groups was initiated in 1969, but the question of whether or not every subgroup of the symmetric group arises as an intrinisic symmetry group of some link has remained open. We provide counterexamples; in particular, if n>5, then there does not exist an n-component link L for which S(L) is the alternating group.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
