Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Kontsevich-Kuperberg-Thurston construction of a
  configuration-space invariant for rational homology 3-spheres   M. Kontsevich proposed a topological construction for an invariant Z of
rational homology 3-spheres using configuration space integrals. G. Kuperberg
and D. Thurston proved that Z is a universal real finite type invariant for
integral homology spheres in the sense of Ohtsuki, Habiro and Goussarov.
  We review the Kontsevich-Kuperberg-Thurston construction and we provide
detailed and elementary proofs for the invariance of Z. This article is the
preliminary part of a work that aims to prove splitting formulae for this
powerful invariant of rational homology spheres. It contains the needed
background for the proof that will appear in the second part.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc