Coarse Geometry and Topological Phases

Abstract

We propose the Roe C∗-algebra from coarse geometry as a model for topological phases of disordered materials. We explain the robustness of this C∗-algebra and formulate the bulk–edge correspondence in this framework. We describe the map from the K-theory of the group C∗-algebra of Zd to the K-theory of the Roe C∗-algebra, both for real and complex K-theory.