论文标题
12倍瓷砖空间的同时组
Cohomology groups for spaces of 12-fold tilings
论文作者
论文摘要
我们考虑使用切割和投影方法获得的12倍对称性的平面砖块。我们使用第二作者Hunton和Kellendonk介绍的技术计算他们的同胞组。为此，我们完全描述了窗口，小组动作下的线条轨道和0个点的轨道。可以使用2-参数来描述完整的概括为12倍砖的家庭，并提出了令人惊讶的富含的共同体结构。为了将此发现置于透视上，应该将我们的结果与普遍的5倍瓷砖（通常称为广义的Penrose Tilings）进行比较。在这种情况下，瓷砖形成了一个1参数家族，它仅适合两种类型的共同体之一。
We consider tilings of the plane with 12-fold symmetry obtained by the cut and projection method. We compute their cohomology groups using the techniques introduced by the second author, Hunton and Kellendonk. To do this we completely describe the window, the orbits of lines under the group action and the orbits of 0-singularities. The complete family of generalized 12-fold tilings can be described using 2-parameters and it presents a surprisingly rich cohomological structure. To put this finding into perspective, one should compare our results with the cohomology of the generalized 5-fold tilings (more commonly known as generalized Penrose tilings). In this case the tilings form a 1-parameter family, which fits in simply one of two types of cohomology.
