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Rotation Numbers, Boundary Forces and Gap labelling

J. Kellendonk·I. P. Zois
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Abstract

We review the Johnson-Moser rotation number and the $K_0$-theoretical gap labelling of Bellissard for one-dimensional Schrödinger operators. We compare them with two further gap-labels, one being related to the motion of Dirichlet eigenvalues, the other being a $K_1$-theoretical gap label. We argue that the latter provides a natural generalisation of the Johnson-Moser rotation number to higher dimensions.

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J. Kellendonk, I. P. Zois. 2005-06-07. Rotation Numbers, Boundary Forces and Gap labelling. https://doi.org/10.1088/0305-4470%2F38%2F18%2F005

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