  We investigate extrinsic wormholelike twist defects that effectively increase
the genus of space in lattice versions of multicomponent fractional quantum
Hall systems. Although the original band structure is distorted by these
defects, leading to localized midgap states, we find that a new lowest flat
band representing a higher genus system can be engineered by tuning local
single-particle potentials. Remarkably, once local many-body interactions in
this new band are switched on, we identify various Abelian and non-Abelian
fractional quantum Hall states, whose ground-state degeneracy increases with
the number of defects, i.e, with the genus of space. This sensitivity of
topological degeneracy to defects provides a "proof of concept" demonstration
that genons, predicted by topological field theory as exotic non-Abelian
defects tied to a varying topology of space, do exist in realistic microscopic
models. Specifically, our results indicate that genons could be created in the
laboratory by combining the physics of artificial gauge fields in cold atom
systems with already existing holographic beam shaping methods for creating
twist defects.
