  We discuss the action of the configuration operators of loop quantum gravity.
In particular, we derive the generalised eigenbasis for the Wilson loop
operator and show that the transformation between this basis and the
spin-network basis is given by an expansion in terms of Chebyshev polynomials.
These results are used to construct states which approximate connections on the
background 3-manifold in an analogous way that the weave states reproduce area
and volumes of a given 3-metric. This should be necessary for the construction
of genuine semi-classical states that are peaked both in the configuration and
momentum variables.

General Relativity and Quantum Cosmology