论文标题
$ sl_n（\ mathbb {k}）$ lattices lot-Global-rigities $
Local-to-Global-rigidity of lattices in $SL_n(\mathbb{K})$
论文作者
论文摘要
如果存在$ r> 0 $，则顶点传递图$ \ MATHCAL {G} $，称为局部到全球刚性，以使每个其他radius $ r $的球都等于radius $ r $ in of Radius $ r $ in $ \ rabscal {G} $覆盖$ \ Mathcal of $ \ nathcal of $ \ nathcal of。 $ psl_n（\ Mathbb {k}）$带有$ n \ geq 4 $和$ \ mathbb {k} $的非Archimedean特征特征零的局部领域。在本文中，我们将这些刚性属性扩展到图形的Quasi-Isote for nottion for n to fortice， $ sl_n（\ mathbb {k}）$。演示是证明建筑物本地结构的机会。我们表明，如果我们修复了$ psl_n（\ mathbb {k}）$ - 轨道，则顶点由该轨道中的相邻顶点唯一确定。
A vertex-transitive graph $\mathcal{G}$ is called Local-to-Global rigid if there exists $R>0$ such that every other graph whose balls of radius $R$ are isometric to the balls of radius $R$ in $\mathcal{G}$ is covered by $\mathcal{G}$. An example of such a graph is given by the Bruhat-Tits building of $PSL_n(\mathbb{K})$ with $n\geq 4$ and $\mathbb{K}$ a non-Archimedean local field of characteristic zero.. In this paper we extend this rigidity property to a class of graphs quasi-isometric to the building including torsion-free lattices of $SL_n(\mathbb{K})$. The demonstration is the occasion to prove a result on the local structure of the building. We show that if we fix a $PSL_n(\mathbb{K})$-orbit in it, then a vertex is uniquely determined by the neighbouring vertices in this orbit.
