  Unoriented SL(3) foams are two-dimensional CW complexes with generic
singularities embedded in 3- and 4-manifolds. They naturally come up in the
Kronheimer-Mrowka SO(3) gauge theory for 3-orbifolds and, in the oriented case,
in a categorification of the Kuperberg bracket quantum invariant. The present
paper studies the more technically complicated case of SL(4) foams.
Combinatorial evaluation of unoriented SL(4) foams is defined and state spaces
for it are studied. In particular, over a suitably localized ground ring, the
state space of any web is free of the rank given by the number of its
4-colorings.
