Topological insulators are materials, which are conducting at
their edges, though not in the bulk. Their characteristic physical
properties are reflected by an index, associated to the Hamiltonian. By
a general principle, known as bulk-edge duality, the index can be
defined either in terms of the bulk or the edge Hamiltonian. Among
various ways of establishing that duality as a theorem, one is by
scattering theory, and in fact by Levinson's theorem.