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Quantum Hall Effect on the Hyperbolic Plane

A. Carey·K. Hannabus·V. Mathai·P. McCann
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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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BibTeXRIS

A. Carey, K. Hannabus, V. Mathai, P. McCann. 1997-04-10. Quantum Hall Effect on the Hyperbolic Plane. https://doi.org/10.1007/s002200050255

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