Questions on Freidel's "Group Field Theory (hep-th/050516)"

In Laurent Freidel's general description of group field theory, http://arxiv.org/abs/hep-th/0505016, which I am studying as preparation for the paper on getting quantum dynamics out of kinematics which was recommended by Helge Rose', I have hit a question. So in case others may want to follow this course to exciting new results, I pose it here, and dignify it with a thread in expectation there will be other questions.
Freidel says:

My question is: how far is this invariance due to features of the Ponzano-Regge model and how far is it a combinatorial expression of the lack of local degrees of freedom in 2-D GR? In general how does the combinatorial structure of a spin-foam model relate to the underlying dynamics on the manifold being represented?

It is basically a combinatorial expression of the lack of local degrees of freedom. The beauty of Ponzano-Regge was in actually constructing such an expression.

Sorry, but your second question is a little vague to me.
Kea