鲍姆斯莱格-索利塔复合物中的不可通约晶格

IF 1 2区数学 Q1 MATHEMATICS Journal of the London Mathematical Society-Second Series Pub Date : 2024-03-08 DOI:10.1112/jlms.12879

Max Forester

{"title":"鲍姆斯莱格-索利塔复合物中的不可通约晶格","authors":"Max Forester","doi":"10.1112/jlms.12879","DOIUrl":null,"url":null,"abstract":"<p>This paper concerns locally finite 2-complexes <math>\n <semantics>\n <msub>\n <mi>X</mi>\n <mrow>\n <mi>m</mi>\n <mo>,</mo>\n <mi>n</mi>\n </mrow>\n </msub>\n <annotation>$X_{m,n}$</annotation>\n </semantics></math> that are combinatorial models for the Baumslag–Solitar groups <math>\n <semantics>\n <mrow>\n <mi>B</mi>\n <mi>S</mi>\n <mo>(</mo>\n <mi>m</mi>\n <mo>,</mo>\n <mi>n</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$BS(m,n)$</annotation>\n </semantics></math>. We show that, in many cases, the locally compact group <math>\n <semantics>\n <mrow>\n <mo>Aut</mo>\n <mo>(</mo>\n <msub>\n <mi>X</mi>\n <mrow>\n <mi>m</mi>\n <mo>,</mo>\n <mi>n</mi>\n </mrow>\n </msub>\n <mo>)</mo>\n </mrow>\n <annotation>$\\operatorname{Aut}(X_{m,n})$</annotation>\n </semantics></math> contains incommensurable uniform lattices. The lattices we construct also admit isomorphic Cayley graphs and are finitely presented, torsion-free, and coherent.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Incommensurable lattices in Baumslag–Solitar complexes\",\"authors\":\"Max Forester\",\"doi\":\"10.1112/jlms.12879\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper concerns locally finite 2-complexes <math>\\n <semantics>\\n <msub>\\n <mi>X</mi>\\n <mrow>\\n <mi>m</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n </mrow>\\n </msub>\\n <annotation>$X_{m,n}$</annotation>\\n </semantics></math> that are combinatorial models for the Baumslag–Solitar groups <math>\\n <semantics>\\n <mrow>\\n <mi>B</mi>\\n <mi>S</mi>\\n <mo>(</mo>\\n <mi>m</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$BS(m,n)$</annotation>\\n </semantics></math>. We show that, in many cases, the locally compact group <math>\\n <semantics>\\n <mrow>\\n <mo>Aut</mo>\\n <mo>(</mo>\\n <msub>\\n <mi>X</mi>\\n <mrow>\\n <mi>m</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n </mrow>\\n </msub>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\operatorname{Aut}(X_{m,n})$</annotation>\\n </semantics></math> contains incommensurable uniform lattices. The lattices we construct also admit isomorphic Cayley graphs and are finitely presented, torsion-free, and coherent.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-03-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12879\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12879","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文涉及局部有限 2 复数 X m , n $X_{m,n}$，它们是鲍姆斯莱格-索利塔群 B S ( m , n ) $BS(m,n)$ 的组合模型。我们证明，在很多情况下，局部紧凑群 Aut ( X m , n ) $\operatorname{Aut}(X_{m,n})$ 包含不可通约的均匀网格。我们所构建的网格还包含同构的卡莱图，并且是有限呈现、无扭转和相干的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Incommensurable lattices in Baumslag–Solitar complexes

This paper concerns locally finite 2-complexes $X_{m, n}$ that are combinatorial models for the Baumslag–Solitar groups $B S (m, n)$ . We show that, in many cases, the locally compact group $Aut (X_{m, n})$ contains incommensurable uniform lattices. The lattices we construct also admit isomorphic Cayley graphs and are finitely presented, torsion-free, and coherent.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.