HALL CONDUCTANCE AS A TOPOLOGICAL INVARIANT

The quantum Hall effect is the precise quantization, in units e(2)/h, of the Hall conductance of a system of charge carriers constrained to move in a plane, with a perpendicular magnetic field. It was discovere d experimentally by von Klitzing et al. in 1980, and successful theori es were put forward soon after. One approach to the theory involves co ncepts of algebraic topology; the Hall conductance is expressed as a t opological invariant called the Chern class. This article is an inform al review of the topological theory of the integer quantum Hall effect , including a non-technical introduction to the mathematical concepts involved.