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

Abstract

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.

arXiv commentLaTex, 71 pages, uses pstricks. Second version of Prepub. Institut Fourier 655 (New title, minor modifications in the abstract and in the introduction.)

References in corpus (2)

• Integral Invariants of 3-Manifolds. II
• Perturbative 3-manifold invariants by cut-and-paste topology

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