AG Mathematische Physik

Gap-filling via coarse geometry

Matthias Ludewig, Regensburg

Abstract: We explain a mathematical framework which uses methods from coarse geometry in order to model topological insulators. In this framework, the boundary behavior is described in terms of exact sequences in operator K-theory. In particular, spectral gap-filling is implied by the non-triviality of a certain K-theoretic boundary map. As an application, this allows to show that the Landau Hamiltonian on a hyperbolic half-plane (and also on more general imperfect half-spaces) has no spectral gaps.