论文标题
与Aperiodic Tilings的衍射和光谱数据有关：朝向Bloch定理
Relating Diffraction and Spectral Data of Aperiodic Tilings: Towards a Bloch theorem
论文作者
论文摘要
本文的目的是显示瓷砖的结构（衍射模式）之间的所有关系（由瓷砖空间的čech共同体描述）与$ k $ - 理论所定义的汉密尔顿人的光谱特性（由汉密尔顿人定义），并在dimensions $ \ leq 3 $中表现出等价。一个定理使这种关系的条件确切化。它可以看作是“ Bloch Theorem”到一大批Aperiodic瓷砖的扩展。该结果的基础的想法是基于共同体与$ k $理论痕迹之间的关系及其在低维度中的等效性。
The purpose of this paper is to show the relationship in all dimensions between the structural (diffraction pattern) aspect of tilings (described by Čech cohomology of the tiling space) and the spectral properties (of Hamiltonians defined on such tilings) defined by $K$-theory, and to show their equivalence in dimensions $\leq 3$. A theorem makes precise the conditions for this relationship to hold. It can be viewed as an extension of the "Bloch Theorem" to a large class of aperiodic tilings. The idea underlying this result is based on the relationship between cohomology and $K$-theory traces and their equivalence in low dimensions.
