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|Title:||Twisted index theory on good orbifolds, II: Fractional quantum numbers|
|Citation:||Communications in Mathematical Physics, 2001; 217(1):55-87|
|Matilde Marcolli, Varghese Mathai|
|Abstract:||This paper uses techniques in noncommutative geometry as developed by Alain Connes [Co2], in order to study the twisted higher index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group, continuing our earlier work [MM]. We also compute the range of the higher cyclic traces on K-theory for cocompact Fuchsian groups, which is then applied to determine the range of values of the Connes–Kubo Hall conductance in the discrete model of the quantum Hall effect on the hyperbolic plane, generalizing earlier results in [Bel+E+S], [CHMM]. The new phenomenon that we observe in our case is that the Connes–Kubo Hall conductance has plateaux at integral multiples of a fractional valued topological invariant, namely the orbifold Euler characteristic. Moreover the set of possible fractions has been determined, and is compared with recently available experimental data. It is plausible that this might shed some light on the mathematical mechanism responsible for fractional quantum numbers.|
|Description:||The original publication can be found at www.springerlink.com|
|Rights:||© Springer-Verlag 2001|
|Appears in Collections:||Aurora harvest 6|
Pure Mathematics publications
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