  We propose a complementary point of view on the topological invariants of
two-dimensional tight-binding models restricted to half-spaces. The transfer
operators for such systems are $J$-unitary on a infinite dimensional Krein
space $(\mathcal{K},J)$ and, for energies in the bulk gap, only have discrete
spectrum on the unit circle. These eigenvalues have Krein inertia which can be
used to define topological invariants determining the nature of the surface
modes and allowing to distinguish different topological phases. This is
illustrated by numerical results.
