球面建筑物等距的子复形与不动点集
Subcomplexes and fixed point sets of isometries of spherical buildings
摘要：
本文研究球形建筑物的凸子复形。我们特别注意球形建筑物保型等距的不动点集。这些集合也是建筑物的自然多面体结构的凸子复形。我们表明，除其他事项外，如果不动点集是顶维的，那么它要么是一个子建筑物或它有外接圆半径$\leq \fracπ{2}$。如果建筑物是类型$A_n$或$D_n$，我们还表明，同样的结论适用于任意（顶维的$D_n$ -情况下）凸子复形。这证明了Kleiner-Leeb在这些情况下的猜想。
英文摘要：
In this paper we study convex subcomplexes of spherical buildings. We pay special attention to fixed point sets of type-preserving isometries of spherical buildings. This sets are also convex subcomplexes of the natural polyhedral structure of the building. We show, among other things, that if the fixed point set is top-dimensional then it is either a subbuilding or it has circumradius $\leq \fracπ{2}$. If the building is of type $A_n$ or $D_n$, we also show that the same conclusion holds for an arbitrary (top-dimensional in the $D_n$-case) convex subcomplex. This proves a conjecture of Kleiner-Leeb in these cases.
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