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Coarse geometry and topological phases. (English) Zbl 07041901
Summary: We propose the Roe \({{\mathrm C}^*}\)-algebra from coarse geometry as a model for topological phases of disordered materials. We explain the robustness of this \({{\mathrm C}^*}\)-algebra and formulate the bulk-edge correspondence in this framework. We describe the map from the K-theory of the group \({{\mathrm C}^*}\)-algebra of \({\mathbb {Z}^d}\) to the K-theory of the Roe \({{\mathrm C}^*}\)-algebra, both for real and complex K-theory.

MSC:
47B Special classes of linear operators
47A General theory of linear operators
47N Miscellaneous applications of operator theory
60H Stochastic analysis
82B Equilibrium statistical mechanics
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