AI 中文总结
本文基于拓扑绝缘体理论思想，利用对称群算子的等变指标在对称破缺时的一致性，建立等变指标的典型弱/强二分法，并探讨其与粗几何指标的关系。
AI 中文摘要
对称群下不变的算子，在任何有限指数子群下也不变。这类算子的等变指标在对称破缺时必须保持一致，我们基于固态物理中拓扑绝缘体理论的思想，运用该原理建立等变指标的典型弱/强二分法，同时研究其与粗几何（宏观）指标的关系。
英文摘要
Operators invariant under a symmetry group are also invariant under any finite-index subgroup. The equivariant indices of such operators must be consistent under symmetry breaking. We use this principle to establish a canonical weak/strong dichotomy for equivariant indices, building on an idea originating in the theory of topological insulators in solid-state physics. We also study the relationship to coarse-geometric, or macroscopic, indices.
