Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Invariant of Integral Homology 3-Spheres Which Is Universal For All
  Finite Type Invariants   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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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics