Topological Crystals: Independence of Spectral Properties with Respect to Reference Systems

It is a common postulate that spectral properties of operators describing physical systems are independent of the underlying reference frames. For the Laplace operator on topological crystals, we prove such a statement from a deeper analysis of the behavior of spectral properties with respect to arbitrary choices. In particular, we investigate the impact of the choice of a unit cell, and of the choice of a family of generators for the transformation group.