Bredon (co)同调、K-(co)同调和Bianchi群中的Hecke算子

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-01-24 DOI:10.1142/s1793525321500606

David Munoz, Jorge Plazas, Mario Vel'asquez

{"title":"Bredon (co)同调、K-(co)同调和Bianchi群中的Hecke算子","authors":"David Munoz, Jorge Plazas, Mario Vel'asquez","doi":"10.1142/s1793525321500606","DOIUrl":null,"url":null,"abstract":"In this paper, we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of Hecke operators for Bianchi groups. Using the Baum–Connes conjecture, we can transfer computations in Bredon homology to obtain a Hecke action on the [Formula: see text]-theory of the reduced [Formula: see text]-algebra of the group. We show the power of this method giving explicit computations for the group [Formula: see text]. In order to carry out these computations we use an Atiyah–Segal type spectral sequence together with the Bredon homology of the classifying space for proper actions.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"113 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Hecke operators in Bredon (co)homology, K-(co)homology and Bianchi groups\",\"authors\":\"David Munoz, Jorge Plazas, Mario Vel'asquez\",\"doi\":\"10.1142/s1793525321500606\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of Hecke operators for Bianchi groups. Using the Baum–Connes conjecture, we can transfer computations in Bredon homology to obtain a Hecke action on the [Formula: see text]-theory of the reduced [Formula: see text]-algebra of the group. We show the power of this method giving explicit computations for the group [Formula: see text]. In order to carry out these computations we use an Atiyah–Segal type spectral sequence together with the Bredon homology of the classifying space for proper actions.\",\"PeriodicalId\":49151,\"journal\":{\"name\":\"Journal of Topology and Analysis\",\"volume\":\"113 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Topology and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793525321500606\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793525321500606","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

本文给出了一个框架，用于研究作用于算术离散群的Bredon (co)同调上的Hecke算子。我们的主要兴趣在于研究Bianchi群的Hecke算子。利用Baum-Connes猜想，我们可以将Bredon同调中的计算转移到群的[公式:见文]-约化[公式:见文]-代数的[理论]- Hecke作用上。我们展示了这种方法的力量，给出了组的显式计算[公式:见文本]。为了进行这些计算，我们使用了一个Atiyah-Segal型谱序列以及固有动作分类空间的Bredon同调。

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

Hecke operators in Bredon (co)homology, K-(co)homology and Bianchi groups

In this paper, we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of Hecke operators for Bianchi groups. Using the Baum–Connes conjecture, we can transfer computations in Bredon homology to obtain a Hecke action on the [Formula: see text]-theory of the reduced [Formula: see text]-algebra of the group. We show the power of this method giving explicit computations for the group [Formula: see text]. In order to carry out these computations we use an Atiyah–Segal type spectral sequence together with the Bredon homology of the classifying space for proper actions.

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

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.