00-266 J. Kellendonk, T. Richter, H. Schulz-Baldes

Edge current channels and Chern numbers in the integer quantum Hall effect (967K, postscript) Jun 16, 00

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Abstract. A quantization theorem for the edge currents is proven for discrete magnetic half-plane operators. Hence the edge channel number is a valid concept also in presence of a disordered potential. Under a gap condition on the corresponding planar model, this quantum number is shown to be equal to the quantized Hall conductivity as given by the Kubo-Chern formula.For the proof of this equality, we consider an exact sequence of C$^*$-algebras (the Toeplitz extension) linking the half-plane and the planar problem, and use a duality theorem for the pairings of $K$-groups with cyclic cohomology.

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