  We investigate the topological phases of two one-dimensional (1D) interacting
superconducting wires and propose topological markers directly measurable from
ground state correlation functions. These quantities remain powerful tools in
the presence of couplings and interactions. We show with the density matrix
renormalization group that the double critical Ising (DCI) phase discovered in
[1] is a fractional topological phase with gapless Majorana modes in the bulk,
and a one-half topological invariant per wire. Using both numerics and quantum
field theoretical methods, we show that the phase diagram remains stable in the
presence of an inter-wire hopping amplitude $t_{\bot}$ at length scales below
$\sim 1/t_{\bot}$. A large inter-wire hopping amplitude results in the
emergence of two integer topological phases, stable also at large interactions.
They host one edge mode per boundary shared between both wires. At large
interactions, the two wires are described by Mott physics, with the $t_{\bot}$
hopping amplitude resulting in a paramagnetic order.
