Quantum Hall Effect on the Hyperbolic Plane |
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Authors: | A. L. Carey K. C. Hannabuss V. Mathai P. McCann |
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Affiliation: | Department of Mathematics, University of Adelaide, Adelaide 5005, Australia.?E-mail: acarey@maths.adelaide.edu.au, vmathai@maths.adelaide.edu.au,?pmccann@maths.adelaide.edu.au, AU Department of Mathematics, University of Oxford, England. E-mail: khannabu@maths.adelaide.edu.au, UK
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Abstract: | In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use the pairing between K-theory and cyclic cohomology theory, to identify this geometric invariant with a topological index, thereby proving the integrality of the Hall conductivity in this case. Received: 17 March 1997 / Accepted: 24 April 1997 |
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