On a Universal Invariant of 3-Manifolds

Thang T. Q. Le; Jun Murakami; Tomotada Ohtsuki

On a Universal Invariant of 3-Manifolds

q-alg 2008-02-03 v1 Quantum Algebra

Authors: Thang T. Q. Le , Jun Murakami , Tomotada Ohtsuki

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.

Keywords

3-manifold invariant Kontsevich integral Kirby calculus Chern-Simons theory Hopf algebra Vassiliev invariant Casson-Walker-Lescop invariant

Cite

@article{arxiv.q-alg/9512002,
  title  = {On a Universal Invariant of 3-Manifolds},
  author = {Thang T. Q. Le and Jun Murakami and Tomotada Ohtsuki},
  journal= {arXiv preprint arXiv:q-alg/9512002},
  year   = {2008}
}

Comments

33 pages, Ams-LaTex, a ready postcript file of the paper is available at http://www.math.buffalo.edu/~letu/

On a Universal Invariant of 3-Manifolds

Abstract

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