{"title":"有限表示群的散度","authors":"N. Brady, H. Tran","doi":"10.4171/ggd/632","DOIUrl":null,"url":null,"abstract":"We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form $r^\\alpha$ for a dense set of exponents $\\alpha \\in [2,\\infty)$ and $r^n\\log(r)$ for integers $n \\geq 2$. The same construction also yields examples of finitely presented groups which contain Morse elements that are not contracting.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2020-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Divergence of finitely presented groups\",\"authors\":\"N. Brady, H. Tran\",\"doi\":\"10.4171/ggd/632\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form $r^\\\\alpha$ for a dense set of exponents $\\\\alpha \\\\in [2,\\\\infty)$ and $r^n\\\\log(r)$ for integers $n \\\\geq 2$. The same construction also yields examples of finitely presented groups which contain Morse elements that are not contracting.\",\"PeriodicalId\":55084,\"journal\":{\"name\":\"Groups Geometry and Dynamics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-02-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Geometry and Dynamics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/ggd/632\",\"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":"Groups Geometry and Dynamics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/ggd/632","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form $r^\alpha$ for a dense set of exponents $\alpha \in [2,\infty)$ and $r^n\log(r)$ for integers $n \geq 2$. The same construction also yields examples of finitely presented groups which contain Morse elements that are not contracting.
期刊介绍：
Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields.
Topics covered include:
geometric group theory;
asymptotic group theory;
combinatorial group theory;
probabilities on groups;
computational aspects and complexity;
harmonic and functional analysis on groups, free probability;
ergodic theory of group actions;
cohomology of groups and exotic cohomologies;
groups and low-dimensional topology;
group actions on trees, buildings, rooted trees.
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