On a Universal Invariant of 3-Manifolds

1995/12/01 by Le, Thang T. Q., Murakami, Jun, Ohtsuki, Tomotada
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.q-alg/9512002

Abstract

We construct an invariant of 3-manifolds using a modification of the Kontsevich integral and Kirby's calculus. This invariant, as expected in perturbative Chern-Simon theory, takes values in the algebra of oriented 3-valent graphs. This algebra is a Hopf algebra, graded by half the number of vertices in 3-valent graphs. The degree 1 term of the invariant coincides with Casson-Walker-Lescop invariant. The degree n term is constructed out of the universal Vassiliev invariant of links of degree less than or equal to (l+1)n where l is the number of link components.

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