和睦相处的希格森日冕团体

arXiv - MATH - Operator Algebras Pub Date : 2024-08-06 DOI:arxiv-2408.02997

Alexander Engel

{"title":"和睦相处的希格森日冕团体","authors":"Alexander Engel","doi":"arxiv-2408.02997","DOIUrl":null,"url":null,"abstract":"We investigate groups that act amenably on their Higson corona (also known as\nbi-exact groups) and we provide reformulations of this in relation to the\nstable Higson corona, nuclearity of crossed products and to positive type\nkernels. We further investigate implications of this in relation to the\nBaum-Connes conjecture, and prove that Gromov hyperbolic groups have isomorphic\nequivariant K-theories of their Gromov boundary and their stable Higson corona.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"104 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Groups acting amenably on their Higson corona\",\"authors\":\"Alexander Engel\",\"doi\":\"arxiv-2408.02997\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate groups that act amenably on their Higson corona (also known as\\nbi-exact groups) and we provide reformulations of this in relation to the\\nstable Higson corona, nuclearity of crossed products and to positive type\\nkernels. We further investigate implications of this in relation to the\\nBaum-Connes conjecture, and prove that Gromov hyperbolic groups have isomorphic\\nequivariant K-theories of their Gromov boundary and their stable Higson corona.\",\"PeriodicalId\":501114,\"journal\":{\"name\":\"arXiv - MATH - Operator Algebras\",\"volume\":\"104 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.02997\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.02997","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

我们研究了可作用于其希格森冕的群组（也称为双作用群组），并结合稳定希格森冕、交叉积的核性和正型核对此进行了重新阐述。我们进一步研究了这一点与鲍姆-康恩猜想（Baum-Connes conjecture）之间的关系，并证明了格罗莫夫双曲群的格罗莫夫边界和稳定希格森冕具有同构向量 K 理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Groups acting amenably on their Higson corona

We investigate groups that act amenably on their Higson corona (also known as bi-exact groups) and we provide reformulations of this in relation to the stable Higson corona, nuclearity of crossed products and to positive type kernels. We further investigate implications of this in relation to the Baum-Connes conjecture, and prove that Gromov hyperbolic groups have isomorphic equivariant K-theories of their Gromov boundary and their stable Higson corona.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Operator Algebras

自引率

0.00%

发文量