  The realization of the Hofstadter model in a strongly anisotropic ladder
geometry has now become possible in one-dimensional optical lattices with a
synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in
such ladder configurations hosts a topological phase of matter which is
radically different from its two-dimensional counterpart. This topological
phase stems directly from the hybrid nature of the ladder geometry, and is
protected by a properly defined inversion symmetry. We start our analysis
considering the paradigmatic case of a three-leg ladder which supports a
topological phase exhibiting the typical features of topological states in one
dimension: robust fermionic edge modes, a degenerate entanglement spectrum and
a non-zero Zak phase; then, we generalize our findings - addressable in the
state-of-the-art cold atom experiments - to ladders with an higher number of
legs.
