{"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":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/proc/16824","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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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