Incommensurable lattices in Baumslag–Solitar complexes

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-03-08 DOI:10.1112/jlms.12879

Max Forester

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Abstract

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.

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鲍姆斯莱格-索利塔复合物中的不可通约晶格

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。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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