{"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}
引用次数: 0
Abstract
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.
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