A three-manifold invariant via the Kontsevich integral
This paper is a starting point for the LMO invariant, a universal perturbative invariant of 3-manifolds [\textit{Thang T. Q. Le, J. Murakami}, and \textit{T. Ohtsuki}, Topology 37, No. 3, 539-574 (1998; Zbl 0897.57017)]. The authors construct an invariant for closed, oriented 3-manifolds based on the Kontsevich integral of framed links [\textit{M. Kontsevich}, Adv. Sov. Math. 16(2), 137-150 (1993; Zbl 0839.57006)]. They describe a different way to normalize the Kontsevich integral, but the definition of the Kontsevich integral is not reviewed in this present paper. Notation and various notations from [\textit{Le Tu Quoc Thang} and \textit{J. Murakami}, Commun. Math. Phys. 168, No. 3, 535-562 (1995; Zbl 0839.57008)] and [\textit{Thang T. Q. Le} and \textit{J. Murakami}, J. Pure Appl. Algebra 121, No. 3, 271-291 (1997; Zbl 0882.57005)] are used without further explanation. The invariant studied in this paper is obtained from the Kontsevich integral by imposing three new relations. The authors show that the invariant defined in this way may be recovered from the order of the first homology and the Lescop generalization of the Casson-Walker invariant. The LMO invariant is further discussed in [\textit{L. Rozansky}, Lect. Notes Pure Appl. Math. 184, 379-397 (1997; Zbl 0868.57014); \textit{S. Garoufalidis} and \textit{J. Levine}, Invent. Math. 131, No. 3, 541-594 (1998; Zbl 0895.57004); \textit{N. Habegger} and \textit{K. E. Orr}, Comment. Math. Helv. 74, No. 2, 322-344 (1999; Zbl 0935.57019)].
scientific article; zbMATH DE number 1445749