Abstract
I review some recent results on canonicalquantum gravity in the spin network representation. Aset of ambient isotopy spin network invariants isintroduced. These invariants are the natural extensionto spin networks of the Vassiliev invariants. Itis shown that this set is loop differentiable in thesense of distributions. The quantum gravity constraintsare written in terms of loop derivatives. It is explicitly shown that Vassiliev invariantssolve the diffeomorphism constraint. The regularizedAshtekar Hamiltonian constraint is studied, and itsaction on valence-four Vassiliev invariantsdiscussed.
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