  We examine the relationship between covariant and canonical
(Ashtekar/Rovelli/Smolin) loop variables in the context of BF type topological
field theories in 2+1 and 3+1 dimensions, with respective gauge groups SO(2,1)
and SO(3,1). The latter model can be considered as the simplest topological
gravity theory in 3+1 dimensions. We carry out the canonical quantization of
this model in both the connection and loop representations, for the two spatial
topologies $T^3$ and $S^2\times S^1$.
