Abstract

We construct an invariant for closed, oriented three-manifolds from the Kontsevich integral of framed links, and show that it includes Lescop's generalization of the Casson-Walker invariant. Combining this result and a formula for computing the Kontsevich integral in [17], we can compute the Casson-Walker invariant combinatorially in terms of q-tangles (non-associative tangles in [3]). Our invariant is obtained from the Kontsevich integral by imposing the threeterm (3T) relation, orientation independence (01) relation, O-vanishing relation and 1-vanishing relation to the space of chord diagrams subjected to the four-term relation. The 3T relation is given by

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