We construct a scattering matrix formulation for the topological index of interacting fermions in one dimension. We show that in the weak coupling limit, the scattering matrix is unitary at zero temperature, and the topological index is restricted  to a finite set of values, $\textrm{Tr}[r_{eh}] \in[-4,4]$. We show that  the two topologically equivalent phases with $\textrm{Tr}[r_{eh}] =4,-4$  are characterized by emergent {\it many-body}  end states, which we identify to be a topologically protected Kondo-like resonance. Finally, we show that 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.