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We propose to interpret the action of the quantum Hamiltonian constraint of general relativity in the loop representation as a skein relation on the space of knots. Therefore, by considering knot polynomials that are compatible with that skein relation, one guarantees that all the quantum Einstein equations are solved. We give a particular example of such an invariant and discuss the consistency of the constraint algebra in this approach. © 1996 IOP Publishing Ltd.

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Classical and Quantum Gravity