Let Z LMO be the 3-manifold invariant of [LMO]. It is shown that Z LMO (M ) = 1, if the first Betti number of M , b 1 (M ), is greater than 3. If b 1 (M ) = 3, then Z LMO (M ) is completely determined by the cohomology ring of M . A relation of Z LMO with the Rozansky-Witten invariants Z RW X [M ] is established at a physical level of rigour. We show that Z RW X [M ] satisfies appropriate connected sum properties suggesting that the generalized Casson invariant ought to be computable from the LMO invariant
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