The Universal Perturbative Quantum 3-manifold Invariant, Rozansky-Witten Invariants, and the Generalized Casson Invariant

الأصل · EN

Let ZLMO be the 3-manifold invariant of [LMO]. It is shown that ZLMO(M)=1, if the first Betti number of M, b₁(M), is greater than 3. If b₁(M)=3, then ZLMO(M) is completely determined by the cohomology ring of M. A relation of ZLMO with the Rozansky-Witten invariants ZₓRW[M] is established at a physical level of rigour. We show that ZₓRW[M] satisfies appropriate connected sum properties suggesting that the generalized Casson invariant ought to be computable from the LMO invariant.