  We show that, quite generically, a [111] slab of spin-orbit coupled
pyrochlore lattice exhibits surface states whose constant energy curves take
the shape of Fermi arcs, localized to different surfaces depending on their
quasimomentum. Remarkably, these persist independently of the existence of Weyl
points in the bulk. Considering interacting electrons in slabs of finite
thickness, we find a plethora of known fractional Chern insulating phases, to
which we add the discovery of a new higher Chern number state which is likely a
generalization of the Moore-Read fermionic fractional quantum Hall state. By
contrast, in the three-dimensional limit, we argue for the absence of gapped
states of the flat surface band due to a topologically protected coupling of
the surface to gapless states in the bulk. We comment on generalizations as
well as experimental perspectives in thin slabs of pyrochlore iridates.
