Boundary maps for $C^*$-crossed products with R with an application to the quantum Hall effect
Mathematical Physics
2016-10-28 v1 math.MP
Abstract
The boundary map in K-theory arising from the Wiener-Hopf extension of a crossed product algebra with R 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 on higher traces (and 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 Schroedinger operators.
Keywords
Cite
@article{arxiv.math-ph/0405022,
title = {Boundary maps for $C^*$-crossed products with R with an application to the quantum Hall effect},
author = {Johannes Kellendonk and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:math-ph/0405022},
year = {2016}
}
Comments
to appear in Commun. Math. Phys