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On a Universal Invariant of 3-Manifolds

Thang T. Q. Le·Jun Murakami·Tomotada Ohtsuki
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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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BibTeXRIS

Thang T. Q. Le, Jun Murakami, Tomotada Ohtsuki. 1995-12-01. On a Universal Invariant of 3-Manifolds. https://arxiv.org/abs/q-alg/9512002

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