04-217 Johannes Kellendonk, Ioannis P Zois

Rotation Numbers, Boundary Forces and Gap Labelling (202K, pdf-file) Jul 16, 04

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Abstract. We review the Johnson-Moser rotation number and the $K_0$-theoretical gap labelling of Bellissard for one-dimensional Schr\"odinger 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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