Quantization of geometry associated to the quantized   Knizhnik-Zamolodchikov equations
  It is known that solutions of the Knizhnik-Zamolodchikov differential equations are given by integrals of closed differential forms over suitable cycles. In this paper a quantization of this geometric construction is described leading to solution of the quantized Knizhnik-Zamolodchikov difference equations. 
Alexander Varchenko