{"title":"关于James Hyde的$\\ mathm {Homeo}(D，\\偏D)$的非有序子群的例子","authors":"Michele Triestino","doi":"10.4171/LEM/66-3/4-5","DOIUrl":null,"url":null,"abstract":"In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of $\\mathrm{Homeo}(D,\\partial D)$, the group of homeomorphisms of the disk fixing the boundary. This implies that the group $\\mathrm{Homeo}(D,\\partial D)$ itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"120 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On James Hyde’s example of non-orderable subgroup of $\\\\mathrm{Homeo}(D,\\\\partial D)$\",\"authors\":\"Michele Triestino\",\"doi\":\"10.4171/LEM/66-3/4-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of $\\\\mathrm{Homeo}(D,\\\\partial D)$, the group of homeomorphisms of the disk fixing the boundary. This implies that the group $\\\\mathrm{Homeo}(D,\\\\partial D)$ itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.\",\"PeriodicalId\":344085,\"journal\":{\"name\":\"L’Enseignement Mathématique\",\"volume\":\"120 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"L’Enseignement Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/LEM/66-3/4-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"L’Enseignement Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/LEM/66-3/4-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On James Hyde’s example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$
In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of $\mathrm{Homeo}(D,\partial D)$, the group of homeomorphisms of the disk fixing the boundary. This implies that the group $\mathrm{Homeo}(D,\partial D)$ itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
