Incommensurable lattices in Baumslag–Solitar complexes

IF 1.2 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

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引用次数: 0

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

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.

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