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Quantum Hall Effect on the Hyperbolic Plane

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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.

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Authors and Affiliations

  1. 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

    A. L. Carey, V. Mathai & P. McCann

  2. Department of Mathematics, University of Oxford, England. E-mail: khannabu@maths.adelaide.edu.au, , , , , , UK

    K. C. Hannabuss

Authors
  1. A. L. Carey
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  2. K. C. Hannabuss
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  3. V. Mathai
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  4. P. McCann
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Received: 17 March 1997 / Accepted: 24 April 1997

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Carey, A., Hannabuss, K., Mathai, V. et al. Quantum Hall Effect on the Hyperbolic Plane . Comm Math Phys 190, 629–673 (1998). https://doi.org/10.1007/s002200050255

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  • DOI: https://doi.org/10.1007/s002200050255

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