Johannes Kellendonk (Lyon)
Abstract: Aperiodic insulators have typically richer topological invariants than periodic ones.
In particular the gap labelling group has more generators. We ask, how we can “measure” the gap labels via spectral flows, like, for instance, the flow of eigenvalues of edge states in one dimensional models. The simple bulk edge correspondence will not do it, because the most interesting models have a discrete hull which is a Cantor set. This was already observed in our earlier work with Emil Prodan on Kohmoto models based on Sturmian sequences. In that work we proposed to augment the hull to make certain flip processes continuous and thereby visible as spectral flow. In this talk I will discuss a generalisation of the above model which has a gap labelling group with one more generator. This generator can be related to a spectral flow density, not of edge states, but of bulk states. When numerically solving the Schroedinger equation to visualise the spectral flow (for a periodic approximation) we face a difficulty: the spectral flow associated with the extra generator obstructs the detection of the edge spectral flow. The solution to this problem is suggested by K-theory: stacking our model with a “topologically trivial” model.
