论文标题
组合高级双曲线条件
A combinatorial higher-rank hyperbolicity condition
论文作者
论文摘要
我们研究了$ 2（n+1）$的粗糙版本 - 点不平等，表征了组合尺寸的度量空间，最多是$ n $。这种情况在实验上称为$（n，δ）$ - 双曲线，如果$ n = 1 $，则将$δ$ hyperbolicity的四倍定义减少到格罗莫夫的四倍定义。 $ l_ \ infty $ - $ n $ $Δ$ - 液体底空间的产品为$（n，δ）$ - 双曲线。每$（n，δ）$ - 双曲线度量空间，没有任何其他假设，都具有纤薄的$（n+1）$ - 单纯属性类似于Gromov双曲线空间中准晶格三角形的微弱性。与几何组理论的最新工作有关，我们表明，每个Helly组和每个分层的双曲线组（渐近）等级$ n $在几何（n，δ）$ - 双曲线空间上几何作用。
We investigate a coarse version of a $2(n+1)$-point inequality characterizing metric spaces of combinatorial dimension at most $n$ due to Dress. This condition, experimentally called $(n,δ)$-hyperbolicity, reduces to Gromov's quadruple definition of $δ$-hyperbolicity in case $n = 1$. The $l_\infty$-product of $n$ $δ$-hyperbolic spaces is $(n,δ)$-hyperbolic. Every $(n,δ)$-hyperbolic metric space, without any further assumptions, possesses a slim $(n+1)$-simplex property analogous to the slimness of quasi-geodesic triangles in Gromov hyperbolic spaces. In connection with recent work in geometric group theory, we show that every Helly group and every hierarchically hyperbolic group of (asymptotic) rank $n$ acts geometrically on some $(n,δ)$-hyperbolic space.
