Coarse geometry and topological phases

TL;DR

This paper introduces the Roe C*-algebra from coarse geometry as a new mathematical framework to model and analyze topological phases in disordered materials, establishing key properties and the bulk-edge correspondence.

Contribution

It formulates a novel approach linking coarse geometry and topological phases, including the robustness of the Roe C*-algebra and the K-theoretic bulk-edge correspondence.

Findings

Established the robustness of the Roe C*-algebra in this context

Formulated the bulk-edge correspondence within the Roe algebra framework

Described the K-theory map from group C*-algebra to Roe C*-algebra for Z^d

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 Z^d to the K-theory of the Roe C*-algebra, both for real and complex K-theory.