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Twisted higher index theory on good orbifolds and fractional quantum numbers

Matilde Marcolli·Varghese Mathai
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Abstract

The twisted Connes-Moscovici higher index theorem is generalized to the case of good orbifolds. The higher index is shown to be a rational number, and in fact non-integer in specific examples of 2-orbifolds. This results in a non-commutative geometry model that predicts the occurrence of fractional quantum numbers in the Hall effect on the hyperbolic plane.

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Matilde Marcolli, Varghese Mathai. 1998-03-12. Twisted higher index theory on good orbifolds and fractional quantum numbers. https://arxiv.org/abs/math/9803051

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