{"title":"某些非自由作用的概有限性与同源性","authors":"E. Ortega, Eduardo Scarparo","doi":"10.4171/ggd/656","DOIUrl":null,"url":null,"abstract":"We show that Cantor minimal $\\mathbb{Z}\\rtimes\\mathbb{Z}_2$-systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal $\\mathbb{Z}\\rtimes\\mathbb{Z}_2$-systems and show that the associated transformation groupoids satisfy the HK conjecture if and only if the action is free.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Almost finiteness and homology of certain non-free actions\",\"authors\":\"E. Ortega, Eduardo Scarparo\",\"doi\":\"10.4171/ggd/656\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that Cantor minimal $\\\\mathbb{Z}\\\\rtimes\\\\mathbb{Z}_2$-systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal $\\\\mathbb{Z}\\\\rtimes\\\\mathbb{Z}_2$-systems and show that the associated transformation groupoids satisfy the HK conjecture if and only if the action is free.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/ggd/656\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/ggd/656","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Almost finiteness and homology of certain non-free actions
We show that Cantor minimal $\mathbb{Z}\rtimes\mathbb{Z}_2$-systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal $\mathbb{Z}\rtimes\mathbb{Z}_2$-systems and show that the associated transformation groupoids satisfy the HK conjecture if and only if the action is free.
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