标题： C*框架用于高阶体-边界对应关系 显示英文标题

标题： C*-framework for higher-order bulk-boundary correspondences

摘要： 典型的晶体是材料的一个有限部分，它可能在某些点对称群下保持不变。 如果它是一个所谓的内在高阶拓扑绝缘体或超导体，那么它会在棱角或角落表现出由晶格对称性和体拓扑保护的边界模式。 我们使用算子K理论来解释这种现象背后的机制。 具体来说，我们推导出一个群胚C*-代数，该代数1）编码了晶体无限尺寸极限下的电子动力学；2）记住了晶体边界处的边界条件，并且3）可以自然地由原子晶格的点对称性作用。 通过闭子集对群胚单位空间的滤过，这些子集在群胚和点群作用下保持不变，提供了群胚C*-代数的等变协滤过。 我们证明了在扭曲等变K理论中诱导的谱序列的特定导出结果枚举了所有非平凡的高阶体-边界对应关系。 显示英文摘要

摘要： A typical crystal is a finite piece of a material which may be invariant under some point symmetry group. If it is a so-called intrinsic higher-order topological insulator or superconductor, then it displays boundary modes at hinges or corners protected by the crystalline symmetry and the bulk topology. We explain the mechanism behind such phenomena using operator K-theory. Specifically, we derive a groupoid C*-algebra that 1) encodes the dynamics of the electrons in the infinite size limit of a crystal; 2) remembers the boundary conditions at the crystal's boundaries, and 3) admits a natural action by the point symmetries of the atomic lattice. The filtrations of the groupoid's unit space by closed subsets that are invariant under the groupoid and point group actions supply equivariant cofiltrations of the groupoid C*-algebra. We show that specific derivations of the induced spectral sequences in twisted equivariant K-theories enumerate all non-trivial higher-order bulk-boundary correspondences.