论文标题
在广义的鲍姆斯拉格 - 统治者组上强烈的Aperiodic sfts
Strongly Aperiodic SFTs on Generalized Baumslag-Solitar groups
论文作者
论文摘要
我们查看基本图形组的基本组群体的构造。特别是我们证明所有广义的鲍姆斯兰 - 统治组（GBS）都承认有强烈的Aperiodic SFT。我们的证明是基于Whyte的结构定理，以及在$ \ Mathbb {f} _n \ times \ times \ Mathbb {z} $和$ bs（m，n）$的两个构造中。我们的两个结构依赖于一种路径折叠技术，该技术在$ \ mathbb {f} _n \ times \ times \ times \ mathbb {z} $上抬高$ \ mathbb {z}^2 $在sft上的sft，或在$ bs（m，n）$上的sft上的双皮动平面上的sft上的sft。在$ \ mathbb {f} _n \ times \ mathbb {z} $的情况下，路径折叠技术也可以保持最小性，因此我们对单型GBS组的sfts aperiodic sfts的最小程度很小。
We look at constructions of aperiodic SFTs on fundamental groups of graph of groups. In particular we prove that all generalized Baumslag-Solitar groups (GBS) admit a strongly aperiodic SFT. Our proof is based on a structural theorem by Whyte and on two constructions of strongly aperiodic SFTs on $\mathbb{F}_n\times \mathbb{Z}$ and $BS(m,n)$ of our own. Our two constructions rely on a path-folding technique that lifts an SFT on $\mathbb{Z}^2$ inside an SFT on $\mathbb{F}_n\times \mathbb{Z}$ or an SFT on the hyperbolic plane inside an SFT on $BS(m,n)$. In the case of $\mathbb{F}_n\times \mathbb{Z}$ the path folding technique also preserves minimality, so that we get minimal strongly aperiodic SFTs on unimodular GBS groups.
