论文标题
kontsevich-zorich单型单构式的翻译盖，某些柏拉图固体的封面
Kontsevich-Zorich monodromy groups of translation covers of some platonic solids
论文作者
论文摘要
我们计算了由某些是出于几何动机的方形表面引起的Kontsevich-Zorich单型组的Zariski闭合。具体而言，我们将出现的三个表面视为柏拉图固体的翻译盖和无限多面体的商的翻译盖，并表明，从每个表面产生的单片组的Zariski闭合等于$ \ rm {sl}的功率（2，2，\ Mathbb {r}）$。 我们使用Matheus-Yoccoz-Zmiaikou定理找到了单型组组的生成器，从而证明了结果，该定理对组的Zariski闭合（以获得“上限”）提供了约束，并分析了Zariski lie代数的维度，以获取Zariski的lie代数（以获取Zariski的关闭（以获得下限）。 此外，将我们的分析与Eskin-Kontsevich-Zorich公式相结合，我们还计算了Kontsevich-Zorich Cocycle的Lyapunov光谱，用于上述方形表面。
We compute the Zariski closure of the Kontsevich-Zorich monodromy groups arising from certain square tiled surfaces that are geometrically motivated. Specifically we consider three surfaces that emerge as translation covers of platonic solids and quotients of infinite polyhedra, and show that the Zariski closure of the monodromy group arising from each surface is equal to a power of $\rm{SL}(2, \mathbb{R})$. We prove our results by finding generators for the monodromy groups, using a theorem of Matheus-Yoccoz-Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound"). Moreover, combining our analysis with the Eskin-Kontsevich-Zorich formula, we also compute the Lyapunov spectrum of the Kontsevich-Zorich cocycle for said square-tiled surfaces.
