A criterion is given for topological stability of Abelian quantum Hall states, and of Luttinger liquids at the boundaries between such states; this suggests a selection rule on states in the quantum Hall hierarchy theory. The linear response of Luttinger liquids to electromagnetic fields is described: the Hall conductance is quantized, irrespective of whether edge modes propagate in different directions.

• Received 23 November 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.2090