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

Kellendonk J, Schulz-Baldes H (2004)

Publication Type: Journal article

Publication year: 2004

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 249

Pages Range: 611-637

Journal Issue: 3

URI: http://de.arxiv.org/abs/math-ph/0405022

DOI: 10.1007/s00220-004-1122-7

Abstract

The boundary map in K-theory arising from the Wiener-Hopf extension of a crossed product algebra with https://static-content.springer.com/image/art%3A10.1007%2Fs00220-004-1122-7/MediaObjects/s00220-004-1122-7flb2.gif 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 Schrödinger operators.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

Cardiff University GB United Kingdom (GB)

How to cite

APA:

Kellendonk, J., & Schulz-Baldes, H. (2004). Boundary maps for C**-crossed products with R with an application to the quantum Hall effect. Communications in Mathematical Physics, 249(3), 611-637. https://dx.doi.org/10.1007/s00220-004-1122-7

MLA:

Kellendonk, Johannes, and Hermann Schulz-Baldes. "Boundary maps for C**-crossed products with R with an application to the quantum Hall effect." Communications in Mathematical Physics 249.3 (2004): 611-637.

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