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

By Nathan Habegger and George Thompson

Abstract

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

Year: 1999
OAI identifier: oai:CiteSeerX.psu:10.1.1.32.3628
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