{"title":"racg的渐近维数的一个新的上界","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":"{\"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}","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}
A new upper bound for the Asymptotic Dimension of RACGs
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.
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