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Mathematical Physics

arXiv:math-ph/0405022 (math-ph)
[Submitted on 7 May 2004]

Title:Boundary maps for $C^*$-crossed products with R with an application to the quantum Hall effect

Authors:Johannes Kellendonk, Hermann Schulz-Baldes
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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 this http URL' 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.
Comments: to appear in Commun. Math. Phys
Subjects: Mathematical Physics (math-ph)
Cite as: arXiv:math-ph/0405022
  (or arXiv:math-ph/0405022v1 for this version)
  https://doi.org/10.48550/arXiv.math-ph/0405022
Journal reference: Commun. Math. Phys. 249, 611-637 (2004)
Related DOI: https://doi.org/10.1007/s00220-004-1122-7

Submission history

From: Hermann Schulz-Baldes [view email]
[v1] Fri, 7 May 2004 08:59:15 UTC (32 KB)
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