  Band-topology is traditionally analyzed in terms of gauge-invariant
observables associated with crystalline Bloch wavefunctions. Recent work has
demonstrated that many of the free fermion topological characteristics survive
even in an amorphous setting. In this work, we extend these studies to
incorporate the effect of strong repulsive interactions on the fate of topology
and other correlation induced phenomena. Using a parton-based approach, we
obtain the interacting phase diagram for an electronic two-orbital model with
tunable topology in a two dimensional amorphous network. In addition to the
(non-)topological phases that are adiabatically connected to the free fermion
limit, we find a number of strongly interacting amorphous analogs of
crystalline Mott insulating phases with non-trivial chiral neutral edge modes,
and a fractionalized Anderson insulating phase. The amorphous networks thus
provide a new playground for studying a plethora of exotic states of matter,
and their glassy dynamics, due to the combined effects of non-trivial topology,
disorder, and strong interactions.
