dorsal/arxiv
View SchemaAn Invariant of Integral Homology 3-Spheres Which Is Universal For All Finite Type Invariants
| Authors | Thang T. Q. Le |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9601002 |
| URL | https://arxiv.org/abs/q-alg/9601002 |
Abstract
In [LMO] a 3-manifold invariant $\Omega(M)$ is constructed using a modification of the Kontsevich integral and the Kirby calculus. The invariant $\Omega$ takes values in a graded Hopf algebra of Feynman 3-valent graphs. Here we show that for homology 3-spheres the invariant $\Omega$ is {\em universal} for all finite type invariants, i.e. $\Omega_n$ is an invariant of order $3n$ which dominates all other invariants of the same order. This shows that the set of finite type invariants of homology 3-spheres is equivalent to the Hopf algebra of Feynman 3-valent graphs. Some corollaries are discussed. A theory of groups of homology 3-spheres, similar to Gusarov's theory for knots, is presented.
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"abstract": "In [LMO] a 3-manifold invariant $\\Omega(M)$ is constructed using a\nmodification of the Kontsevich integral and the Kirby calculus. The invariant\n$\\Omega$ takes values in a graded Hopf algebra of Feynman 3-valent graphs. Here\nwe show that for homology 3-spheres the invariant $\\Omega$ is {\\em universal}\nfor all finite type invariants, i.e. $\\Omega_n$ is an invariant of order $3n$\nwhich dominates all other invariants of the same order. This shows that the set\nof finite type invariants of homology 3-spheres is equivalent to the Hopf\nalgebra of Feynman 3-valent graphs. Some corollaries are discussed. A theory of\ngroups of homology 3-spheres, similar to Gusarov\u0027s theory for knots, is\npresented.",
"arxiv_id": "q-alg/9601002",
"authors": [
"Thang T. Q. Le"
],
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"q-alg",
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"title": "An Invariant of Integral Homology 3-Spheres Which Is Universal For All Finite Type Invariants",
"url": "https://arxiv.org/abs/q-alg/9601002"
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