{"title":"一般康托尔行动的渐近维度和超有限性","authors":"Sumun Iyer, Forte Shinko","doi":"arxiv-2409.03078","DOIUrl":null,"url":null,"abstract":"We show that for a countable discrete group which is locally of finite\nasymptotic dimension, the generic continuous action on Cantor space has\nhyperfinite orbit equivalence relation. In particular, this holds for free\ngroups, answering a question of Frisch-Kechris-Shinko-Vidny\\'anszky.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic dimension and hyperfiniteness of generic Cantor actions\",\"authors\":\"Sumun Iyer, Forte Shinko\",\"doi\":\"arxiv-2409.03078\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that for a countable discrete group which is locally of finite\\nasymptotic dimension, the generic continuous action on Cantor space has\\nhyperfinite orbit equivalence relation. In particular, this holds for free\\ngroups, answering a question of Frisch-Kechris-Shinko-Vidny\\\\'anszky.\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.03078\",\"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 - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.03078","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Asymptotic dimension and hyperfiniteness of generic Cantor actions
We show that for a countable discrete group which is locally of finite
asymptotic dimension, the generic continuous action on Cantor space has
hyperfinite orbit equivalence relation. In particular, this holds for free
groups, answering a question of Frisch-Kechris-Shinko-Vidny\'anszky.