Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in [Formula: see text]-theory. The other type is by module multiplications in [Formula: see text]-theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Higson corona.

中文翻译：

---

扭曲算子的粗略指数

介绍了几种计算扭曲狄拉克类型算子粗指数的公式。一类这样的公式是由[公式：见正文]-理论中的组成产品。另一种类型是[公式：见正文]理论中的模乘法，它也产生了对 Roe 代数和稳定 Higson 电晕之间对偶性的指数理论解释。