We estimate the number of simplices required for triangulations of compact Lie groups. As in the previous work [12], our approach combines the estimation of the number of vertices by means of the covering type via a cohomological argument from [11], and application of the recent versions of the Lower Bound Theorem of combinatorial topology. For the exceptional Lie groups, we present a complete calculation using the description of their cohomology rings given by the first and third authors. For the infinite series of classical Lie groups of growing dimension d, we estimate the growth rate of number of simplices of the highest dimension, which extends to the case of simplices of (fixed) codimension $d-i$.

我们估计紧凑李群的三角剖分所需的单纯形数量。如先前的工作[12]中所述，我们的方法结合了通过[11]中的同调论据通过覆盖类型对顶点数量的估计以及组合拓扑的下界定理的最新版本的应用。对于特殊的李群，我们使用第一作者和第三作者给出的同调环描述来进行完整的计算。对于维数为d的无穷经典Lie群的无穷系列，我们估计了最大维数的单纯形数量的增长率，这种增长率扩展到（固定）维数的单纯形的情况$d-\mathrm{一世}$。