  We construct a scattering matrix formulation for the topological
classification of one-dimensional superconductors with effective time reversal
symmetry in the presence of interactions. For a closed geometry, Fidkowski and
Kitaev have shown that such systems have a $\mathbb{Z}_8$ topological
classification. We show that in the weak coupling limit, these systems retain a
unitary scattering matrix at zero temperature, with a topological index given
by the trace of the Andreev reflection matrix, $\mbox{tr}\, r_{\rm he}$. With
interactions, $\mbox{tr}\, r_{\rm he}$ generically takes on the finite set of
values $0$, $\pm 1$, $\pm 2$, $\pm 3$, and $\pm 4$. We show that the two
topologically equivalent phases with $\mbox{tr}\, r_{\rm he} = \pm 4$ support
emergent many-body end states, which we identify to be a topologically
protected Kondo-like resonance. The path in phase space that connects these
equivalent phases crosses a non-fermi liquid fixed point where a multiple
channel Kondo effect develops. Our results connect the topological index to
transport properties, thereby highlighting the experimental signatures of
interacting topological phases in one dimension.
