Twisted higher index theory on good orbifolds and fractional quantum   numbers
  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. 
Matilde Marcolli (MIT) and Varghese Mathai (University of Adelaide)