The Topology of Mobility-Gapped Insulators

Jacob Shapiro

Published 2018-11-19, updated 2019-08-13Version 2

Studying deterministic operators, we define an appropriate topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall effect, and lastly we show why our "insulator" condition makes sense from the point of view of the localization theory using the fractional moments method.