Cat(0)多边形配合物为2中位数

Pub Date : 2023-10-24 DOI:10.1007/s10711-023-00841-8
Shaked Bader, Nir Lazarovich
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引用次数: 0

摘要

中位数空间是每三个点之间的三个间隔相交于一个点的空间。众所周知,1级仿射建筑是中位数空间,但由于Haettel,更高级别的建筑甚至不是粗中位数。我们定义了“2-中位数空间”的概念,粗略地说,对于每四个点,填充四个测地线三角形的最小圆盘相交于一个点或测地线段。我们证明了CAT(0)欧几里得多边形复合物,特别是2阶仿射建筑物,是2中位数的。在附录中,我们恢复了法里-米尔诺型定理的Stadler结果的一个特例,并在初等工具中证明了填充测地三角形的极小圆盘是内射的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Cat(0) polygonal complexes are 2-median

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Cat(0) polygonal complexes are 2-median
Abstract Median spaces are spaces in which for every three points the three intervals between them intersect at a single point. It is well known that rank-1 affine buildings are median spaces, but by a result of Haettel, higher rank buildings are not even coarse median. We define the notion of “2-median space”, which roughly says that for every four points the minimal discs filling the four geodesic triangles they span intersect in a point or a geodesic segment. We show that CAT(0) Euclidean polygonal complexes, and in particular rank-2 affine buildings, are 2-median. In the appendix, we recover a special case of a result of Stadler of a Fary–Milnor type theorem and show in elementary tools that a minimal disc filling a geodesic triangle is injective.
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