可解鲍姆斯莱格-索利塔网格

arXiv - MATH - Group Theory Pub Date : 2024-08-23 DOI:arxiv-2408.13381

Noah Caplinger

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引用次数: 0

摘要

可解的鲍姆斯拉格索利塔群 $\text{BS}(1,n)$ 都包含一个规范模型空间 $X_n$。我们给出了 $G_n =\text{Isom}^+(X_n)$ 中网格的完整分类，并发现这些网格不具有强刚性$unicode{x2014}$，存在网格 $\Gamma \子集 G_n$ 的自动变形，它们不扩展到 $G_n$，但满足较弱形式的刚性：对于所有同构的网格 $\Gamma_1,\Gamma_2\subset G_n$来说，在 \text{Aut}(G_n)$ 中存在一个自变量 $\rho ，这样 $\rho(\Gamma_1) = \Gamma_2$.

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Solvable Baumslag-Solitar Lattices

The solvable Baumslag Solitar groups $\text{BS}(1,n)$ each admit a canonical model space, $X_n$. We give a complete classification of lattices in $G_n = \text{Isom}^+(X_n)$ and find that such lattices fail to be strongly rigid$\unicode{x2014}$there are automorphisms of lattices $\Gamma \subset G_n$ which do not extend to $G_n$$\unicode{x2014}$but do satisfy a weaker form of rigidity: for all isomorphic lattices $\Gamma_1,\Gamma_2\subset G_n$, there is an automorphism $\rho \in \text{Aut}(G_n)$ so that $\rho(\Gamma_1) = \Gamma_2$.

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arXiv - MATH - Group Theory

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