  We address the topological classification of one-dimensional chiral symmetric
interfaces embedded into a two-dimensional substrate. A proof of the validity
of a topological classification based on the Green's function by explicit
evaluation of the topological invariant is presented. Further, we show that due
to entanglement between the in-gap modes and the substrate, the full physics of
the substrate that is contained in the Green's function is required. This is
done by considering a classification scheme derived from the reduced ground
state projector, for which we show that an uncritical handling produces
erroneous changes in the topological index due to entanglement driven gap
closures. We illustrate our results by applying them to a tight-binding model
of a spiral magnetic interface in a s-wave superconductor.
