  We state and prove a general result establishing that T-duality simplifies
the bulk-boundary correspondence, in the sense of converting it to a simple
geometric restriction map. This settles in the affirmative several earlier
conjectures of the authors, and provides a clear geometric picture of the
correspondence. In particular, our result holds in arbitrary spatial dimension,
in both the real and complex cases, and also in the presence of disorder,
magnetic fields, and H-flux. These special cases are relevant both to String
Theory and to the study of the quantum Hall effect and topological insulators
with defects in Condensed Matter Physics.
