{"title":"群与单关系群图的渐近维数","authors":"Panagiotis Tselekidis","doi":"10.2140/agt.2023.23.3587","DOIUrl":null,"url":null,"abstract":"We prove a new inequality for the asymptotic dimension of HNN-extensions. We deduce that the asymptotic dimension of every one relator group is at most two, confirming a conjecture of A.Dranishnikov. As another corollary we calculate the exact asymptotic dimension of Right-angled Artin groups. We prove a new upper bound for the asymptotic dimension of fundamental groups of graphs of groups. This leads to a partial result on the asymptotic Morita conjecture for finitely generated groups.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Asymptotic dimension of graphs of groups and one-relator groups\",\"authors\":\"Panagiotis Tselekidis\",\"doi\":\"10.2140/agt.2023.23.3587\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a new inequality for the asymptotic dimension of HNN-extensions. We deduce that the asymptotic dimension of every one relator group is at most two, confirming a conjecture of A.Dranishnikov. As another corollary we calculate the exact asymptotic dimension of Right-angled Artin groups. We prove a new upper bound for the asymptotic dimension of fundamental groups of graphs of groups. This leads to a partial result on the asymptotic Morita conjecture for finitely generated groups.\",\"PeriodicalId\":50826,\"journal\":{\"name\":\"Algebraic and Geometric Topology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic and Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2023.23.3587\",\"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":"Algebraic and Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.3587","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Asymptotic dimension of graphs of groups and one-relator groups
We prove a new inequality for the asymptotic dimension of HNN-extensions. We deduce that the asymptotic dimension of every one relator group is at most two, confirming a conjecture of A.Dranishnikov. As another corollary we calculate the exact asymptotic dimension of Right-angled Artin groups. We prove a new upper bound for the asymptotic dimension of fundamental groups of graphs of groups. This leads to a partial result on the asymptotic Morita conjecture for finitely generated groups.
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