  The integral quantum Hall effect can be explained either as resulting from
bulk or edge currents (or, as it occurs in real samples, as a combination of
both). This leads to different definitions of Hall conductance, which agree
under appropriate hypotheses, as shown by Schulz-Baldes et al. by means of
K-theory. We propose an alternative proof based on a generalization of the
index of a pair of projections to more general operators. The equality of
conductances is an expression of the stability of that index as a flux tube is
moved from within the bulk across the boundary of a sample.
