Topological invariants for substitution tilings and their associated $C^\ast$-algebras
Topological invariants for substitution tilings and their associated $C^\ast$-algebras
复制标题
替换平铺的拓扑不变量及其相关的 $C^ast$-代数
DOI：
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发表时间：
1998
影响因子：
0.9
通讯作者：
I. Putnam
中科院分区：
文献类型：
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作者：
Jared E. Anderson;I. Putnam
我们考虑由替换镶嵌产生的动力系统。在一定的假设下，我们证明了镶嵌空间上的置换映射或膨胀映射的动力学拓扑共轭于一个平稳逆极限上的位移，即R。F.威廉姆斯的广义线性方程。逆极限构造中的底层空间在大多数例子中很容易计算，并且经常具有CW-复形的结构。这使我们能够计算的上同调和K-理论的空间的平铺。这是完全为几个一维和二维平铺，包括彭罗斯平铺。该方法还允许计算用于替代的zeta函数。我们讨论了与这些动力系统相关的C^*$-代数，并展示了如何使用上述方法来计算这些动力系统的K-理论。
We consider the dynamical systems arising from substitution tilings. Under some hypotheses, we show that the dynamics of the substitution or inflation map on the space of tilings is topologically conjugate to a shift on a stationary inverse limit, i.e. one of R. F. Williams' generalized solenoids. The underlying space in the inverse limit construction is easily computed in most examples and frequently has the structure of a CW-complex. This allows us to compute the cohomology and K-theory of the space of tilings. This is done completely for several one- and two-dimensional tilings, including the Penrose tilings. This approach also allows computation of the zeta function for the substitution. We discuss $C^*$-algebras related to these dynamical systems and show how the above methods may be used to compute the K-theory of these.