03-367 J. Kellendonk, H. Schulz-Baldes

Boundary maps for C*-crossed products with R with an application to the quantum Hall effect (587K, postscript) Aug 14, 03

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Abstract. The boundary map in K-theory arising from the Wiener-Hopf extension of a crossed product algebra with $\RR$ is the Connes-Thom isomorphism. In this article, the Wiener Hopf extension is combined with the Heisenberg group algebra to provide an elementary construction of a corresponding map in cyclic cohomology. It then follows directly from a non-commutative Stokes theorem that this map is dual w.r.t. Connes' pairing of cyclic cohomology with K-theory. As an application, we prove equality of quantized bulk and edge conductivities for the integer quantum Hall effect described by continuous magnetic Schrodinger operators.

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