Topological Investigation of the Fractionally Quantized Hall Conductivity

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 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.