Universal invariants, the Conway polynomial and the Casson-Walker-Lescop invariant

Abstract: We give a general surgery formula for the Casson-Walker-Lescop invariant of closed 3-manifolds, seen as the leading term of the LMO invariant, in a purely diagrammatic and combinatorial way. This provides a new viewpoint on a formula established by C. Lescop for her extension of the Walker invariant. A central ingredient in our proof is an explicit identification of the coefficients of the Conway polynomial as combinations of coefficients in the Kontsevich integral. This latter result relies on general \lq factorization formulas\rq\, for the Kontsevich integral coefficients.