{"title":"紧凑度量空间上有限生成群的作用","authors":"Ursula Hamenstädt","doi":"10.1090/proc/16865","DOIUrl":null,"url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Γ</mml:mi> <mml:annotation encoding=\"application/x-tex\">\\Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a finitely generated group which admits an action by homeomorphisms on a metrizable space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that there is a metric on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> defining the original topology such that for this metric, the action is by bi-Lipschitz transformations.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Actions of finitely generated groups on compact metric spaces\",\"authors\":\"Ursula Hamenstädt\",\"doi\":\"10.1090/proc/16865\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"normal upper Gamma\\\"> <mml:semantics> <mml:mi mathvariant=\\\"normal\\\">Γ</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">\\\\Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a finitely generated group which admits an action by homeomorphisms on a metrizable space <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper X\\\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that there is a metric on <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper X\\\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> defining the original topology such that for this metric, the action is by bi-Lipschitz transformations.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/proc/16865\",\"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/10.1090/proc/16865","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
让 Γ \Gamma 是一个有限生成的群，它在可元空间 X X 上允许同构作用。我们将证明在 X X 上存在一个定义了原始拓扑的度量，对于这个度量，作用是通过双利普西茨变换实现的。
Actions of finitely generated groups on compact metric spaces
Let Γ\Gamma be a finitely generated group which admits an action by homeomorphisms on a metrizable space XX. We show that there is a metric on XX defining the original topology such that for this metric, the action is by bi-Lipschitz transformations.
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