  Toward defining commutative cubes in all dimensions, Brown and Spencer
introduced the notion of "connection" as a new kind of degeneracy. In this
paper, for a cubical set with connections, we show that the connections
generate an acyclic subcomplex of the chain complex of the cubical set. In
particular, our results show that the homology groups of a cubical set with
connections are independent of whether we normalize by the connections or we do
not, that is, connections do not contribute to any nontrivial cycle in the
homology groups of the cubical set.
