# Gap Labelling for Discrete One-Dimensional Ergodic Schr\"odinger Operators

@inproceedings{Damanik2022GapLF, title={Gap Labelling for Discrete One-Dimensional Ergodic Schr\"odinger Operators}, author={David Damanik and Jake Fillman}, year={2022} }

In this survey, we give an introduction to and proof of the gap labelling theorem for discrete one-dimensional ergodic Schrödinger operators via the Schwartzman homomorphism. To keep the paper relatively self-contained, we include background on the integrated density of states, the oscillation theorem for 1D operators, and the construction of the Schwartzman homomorphism. We illustrate the result with some examples. In particular, we show how to use the Schwartzman formalism to recover the…

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