On the Kontsevich-Kuperberg-Thurston construction of a configuration-space invariant for rational homology 3-spheres

Details On the Kontsevich-Kuperberg-Thurston construction of a configuration-space invariant for rational homology 3-spheres On the Kontsevich-Kuperberg-Thurston construction of a configuration-space invariant for rational homology 3-spheres

2004-11-04

arxiv.org/abs/math/0411088v1

Mathematics

Geometric Topology

LaTex, 71 pages, uses pstricks. Second version of Prepub. Institut Fourier 655 (New title, minor modifications in the abstract

Scientific paper

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.

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