[en] In this paper we give a necessary condition in order for a geometrical surface to allow for Abelian fractional statistics. In particular, we show that such statistics is possible only for two-dimentional oriented surfaces of genus zero, namely the sphere S2, the plane R2 and the cylindrical surface R1*S1, and in general the connected sum of n planes R2-R2-R2-...-R2. (Author)