{"title":"Amenability problem for Thompson's group $F$: state of the art","authors":"Guba, Victor","doi":"10.46298/jgcc.2023.15.1.11315","DOIUrl":null,"url":null,"abstract":"This is a survey of our recent results on the amenability problem for Thompson's group $F$. They mostly concern esimating the density of finite subgraphs in Cayley graphs of $F$ for various systems of generators, and also equations in the group ring of $F$. We also discuss possible approaches to solve the problem in both directions.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"17 1","pages":"0"},"PeriodicalIF":0.1000,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/jgcc.2023.15.1.11315","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This is a survey of our recent results on the amenability problem for Thompson's group $F$. They mostly concern esimating the density of finite subgraphs in Cayley graphs of $F$ for various systems of generators, and also equations in the group ring of $F$. We also discuss possible approaches to solve the problem in both directions.
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