AI 中文总结
研究欧几里得建筑中余紧格边界作用的稳定性，通过考虑等距离散群作用的扰动，证明足够小扰动与原始作用半共轭，得出半单\(p\) - 进李群中余紧格在\(G/Q\)上有拓扑稳定作用的结论。
AI 中文摘要
当\(X\)是局部紧欧几里得建筑时，\(X\)的等距群通过同胚作用于\(X\)视觉边界中的\(k\) - 单形空间。我们考虑在\(X\)上紧致商作用的等距离散群的这些作用的扰动，表明所有足够小的扰动与原始作用半共轭。特别证明了当\(Q\)是半单\(p\) - 进李群\(G\)中的任何抛物子群时，\(G\)中余紧格的诱导作用在\(G/Q\)上有拓扑稳定作用。
英文摘要
When $X$ is a locally compact Euclidean building, the isometry group of $X$ acts by homeomorphisms on the space of $k$-simplices in the visual boundary of $X$. We consider perturbations of these actions for discrete groups of isometries acting with compact quotient on $X$, showing that all small enough perturbations are semi-conjugate to the original action. This proves in particular that, when $Q$ is any parabolic subgroup in a semisimple $p$-adic Lie group $G$, the induced action of a cocompact lattice in $G$ has a topologically stable action on $G/Q$.
Comments37 pages; comments are welcome
