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

1999/11/08 by Nathan Habegger, Habegger, Nathan, G.E. Thompson +2
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #hep-th #math.GT

paper · pdf · doi:10.48550/arxiv.math/9911049

LaTex 62 pages with 4 figures

arxiv created 1999/11/08 · openalex publication_date 1999/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, b₁(M), is greater than 3. If b₁(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_X^RW[M] is established at a physical level of rigour. We show that Z_X^RW[M] satisfies appropriate connected sum properties suggesting that the generalized Casson invariant ought to be computable from the LMO invariant.

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