{"title":"罗伊函数保持同顶性","authors":"Georgii Makeev","doi":"10.1090/proc/16824","DOIUrl":null,"url":null,"abstract":"<p>We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^{*}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebras and prove that this correspondence is invariant with respect to coarse homotopies.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Roe functors preserve homotopies\",\"authors\":\"Georgii Makeev\",\"doi\":\"10.1090/proc/16824\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper C Superscript asterisk\\\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\\\"application/x-tex\\\">C^{*}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebras and prove that this correspondence is invariant with respect to coarse homotopies.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-09\",\"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/16824\",\"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/16824","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
我们证明，有界几何的可数度量空间之间的粗映射会诱发 C ∗ C^{*} 的足够好的内函数的自然变换，并证明这种对应关系在粗同调方面是不变的。 -代数，并证明这种对应关系在粗同调方面是不变的。
We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of C∗C^{*}-algebras and prove that this correspondence is invariant with respect to coarse homotopies.
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