{"title":"A new upper bound for the Asymptotic Dimension of RACGs","authors":"Panagiotis Tselekidis","doi":"10.4153/s0008439523000760","DOIUrl":null,"url":null,"abstract":"Abstract Let $W_{\\Gamma} $ be the right-angled Coxeter group with defining graph $\\Gamma $ . We show that the asymptotic dimension of $W_{\\Gamma} $ is smaller than or equal to $\\mathrm{dim}_{CC}(\\Gamma )$ , the clique-connected dimension of the graph. We generalize this result to graph products of finite groups.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4153/s0008439523000760","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Let $W_{\Gamma} $ be the right-angled Coxeter group with defining graph $\Gamma $ . We show that the asymptotic dimension of $W_{\Gamma} $ is smaller than or equal to $\mathrm{dim}_{CC}(\Gamma )$ , the clique-connected dimension of the graph. We generalize this result to graph products of finite groups.