The Casson–Walker–Lescop Invariant as a Quantum 3-manifold Invariant

Let Z(M) be the 3-manifold invariant of Le, Murakami and Ohtsuki. We give a direct computational proof that the degree 1 part of Z(M) satisfies , where b₁(M) denotes the first Betti number of M and where λ_M denotes the Lescop generalization of the Casson-Walker invariant of M. Moreover, if b₁(M)=2, we show that Z(M) is determined by λ_M.