论文标题
随机二维大型拓扑和几何形状
Topology and geometry of random 2-dimensional hypertrees
论文作者
论文摘要
Hypertree或$ \ Mathbb {Q} $ - 环体复合物是树的较高维度类似物。我们根据里昂建议的决定性措施来研究随机$ 2 $维度的大型夫人。我们对它们的拓扑和几何特性特别感兴趣。我们表明，有了很高的概率，随机的$ 2 $二维的hamprete $ t $是辅助性的，即它具有合同的通用覆盖范围。我们还表明，具有高概率的基本组$π_1（t）$是双曲线，并具有共生尺寸$ 2 $。
A hypertree, or $\mathbb{Q}$-acyclic complex, is a higher-dimensional analogue of a tree. We study random $2$-dimensional hypertrees according to the determinantal measure suggested by Lyons. We are especially interested in their topological and geometric properties. We show that with high probability, a random $2$-dimensional hypertree $T$ is apsherical, i.e. that it has a contractible universal cover. We also show that with high probability the fundamental group $π_1(T)$ is hyperbolic and has cohomological dimension $2$.
