考克斯特群、双曲立方体和锐角三角剖分
Coxeter groups, hyperbolic cubes, and acute triangulations
摘要：
设$C(L)$是由$\mathbb{S}^2$的抽象三角剖分$L$定义的直角Coxeter群。证明了$C(L)$同构于双曲直角反射群的充要条件是$L$可实现为锐角三角剖分。证明依赖于CAT（-1）空间的理论。一个推论是，当$\mathbb{S}^2$的抽象三角剖分满足一个称为“标志非正方形”的组合条件时，它可以精确地实现为锐角三角剖分。我们还研究了这一结果的推广到其他角度的界限，其他平面表面和其他尺寸。
英文摘要：
Let $C(L)$ be the right-angled Coxeter group defined by an abstract triangulation $L$ of $\mathbb{S}^2$. We show that $C(L)$ is isomorphic to a hyperbolic right-angled reflection group if and only if $L$ can be realized as an acute triangulation. The proof relies on the theory of CAT(-1) spaces. A corollary is that an abstract triangulation of $\mathbb{S}^2$ can be realized as an acute triangulation exactly when it satisfies a combinatorial condition called "flag no-square". We also study generalizations of this result to other angle bounds, other planar surfaces and other dimensions.
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