  Using the fiber bundle concept developed in geometry and topology, the
fractionally quantized Hall conductivity is discussed in the relevant
many--particle configuration space. Electron-magnetic field and
electron-electron interactions under FQHE conditions are treated as functional
connections over the torus, the torus being the underlying two-dimensional
manifold. Relations to the $(2+1)$--dimensional Chern--Simons theory are
indicated. The conductivity being a topological invariant is given as
$\frac{e^2}{h}$ times a linking number which is the quotient of the winding
numbers of the self-consistent field and the magnetic field, respectively. Odd
denominators are explained by the two spin structures which have been
considered for the FQHE correlated electron system.
