匹配规则的上同调

摘要：

拟周期图案描述的多面体“原子表面”和承认匹配规则被认为是。它表明，这种模式的连续壳的上同调环同构的补充环面$T^N$的安排$A$加厚仿射环面的余维2。显式计算贝蒂数的几个二维瓷砖和二十面体的阿曼-克莱默瓷砖证实了在大多数情况下，以前通过不同的方法得到的结果。$T^N \backslash A$的上同调群在模式的空间对称群的群环上具有右模的自然结构，并且可以分解为它的不可约表示的直和。这样的分解的一个例子是Ammann-Kramer平铺。

英文摘要：

Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus $T^N$ to an arrangement $A$ of thickened affine tori of codimension two. Explicit computation of Betti numbers for several two-dimensional tilings and for the icosahedral Ammann-Kramer tiling confirms in most cases the results obtained previously by different methods. The cohomology groups of $T^N \backslash A$ have a natural structure of a right module over the group ring of the space symmetry group of the pattern and can be decomposed in a direct sum of its irreducible representations. An example of such decomposition is shown for the Ammann-Kramer tiling.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。