Abstract
We have performed an experiment in the quantum Hall regime using a geometry that has connectivity between two and three depending on the applied gate voltage. The measurements may be interpreted in terms of either bulk or edge transport. However, the variable connectivity reveals fundamental differences in the current flow through the gated region in the two pictures. In the edge picture this current does not link the measurement contacts and is dissipationless; in the bulk picture it links the contacts and requires dissipation to flow. This extends previous results on the equivalence of the two pictures in simply connected geometries. \textcopyright{} 1996 The American Physical Society.
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