图群的Matui的AH猜想

IF 0.9 3区数学 Q2 MATHEMATICS

Documenta Mathematica Pub Date : 2020-03-31 DOI:10.4171/dm/853

P. Nyland, E. Ortega

{"title":"图群的Matui的AH猜想","authors":"P. Nyland, E. Ortega","doi":"10.4171/dm/853","DOIUrl":null,"url":null,"abstract":"We prove that Matui's AH conjecture holds for graph groupoids of infinite graphs. This is a conjecture which relates the topological full group of an ample groupoid with the homology of the groupoid. Our main result complements Matui's result in the finite case, which makes the AH conjecture true for all graph groupoids covered by the assumptions of said conjecture. Furthermore, we observe that for arbitrary graphs, the homology of a graph groupoid coincides with the $K$-theory of its groupoid $C^*$-algebra.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"56 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Matui's AH conjecture for graph groupoids\",\"authors\":\"P. Nyland, E. Ortega\",\"doi\":\"10.4171/dm/853\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that Matui's AH conjecture holds for graph groupoids of infinite graphs. This is a conjecture which relates the topological full group of an ample groupoid with the homology of the groupoid. Our main result complements Matui's result in the finite case, which makes the AH conjecture true for all graph groupoids covered by the assumptions of said conjecture. Furthermore, we observe that for arbitrary graphs, the homology of a graph groupoid coincides with the $K$-theory of its groupoid $C^*$-algebra.\",\"PeriodicalId\":50567,\"journal\":{\"name\":\"Documenta Mathematica\",\"volume\":\"56 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-03-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Documenta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/dm/853\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Documenta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/dm/853","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: 5

摘要

证明了Matui的AH猜想对于无限图的图群是成立的。这是一个将一个样本群的拓扑满群与群的同调联系起来的猜想。我们的主要结果补充了Matui在有限情况下的结果，使得AH猜想对所有被该猜想的假设覆盖的图群都成立。进一步，我们观察到对于任意图，图群的同调性与群的C^*$代数的K$-理论一致。

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

Matui's AH conjecture for graph groupoids

We prove that Matui's AH conjecture holds for graph groupoids of infinite graphs. This is a conjecture which relates the topological full group of an ample groupoid with the homology of the groupoid. Our main result complements Matui's result in the finite case, which makes the AH conjecture true for all graph groupoids covered by the assumptions of said conjecture. Furthermore, we observe that for arbitrary graphs, the homology of a graph groupoid coincides with the $K$-theory of its groupoid $C^*$-algebra.

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

Documenta Mathematica 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： DOCUMENTA MATHEMATICA is open to all mathematical fields und internationally oriented Documenta Mathematica publishes excellent and carefully refereed articles of general interest, which preferably should rely only on refereed sources and references.