Splitting formulae for the Kontsevich-Kuperberg-Thurston invariant of 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 discuss the behaviour of Z under rational homology handlebodies replacements. The explicit formulae that we present generalize a sum formula obtained by the author for the Casson-Walker invariant in 1994. They allow us to identify the degree one term of Z with the Walker invariant for rational homology spheres.

LaTex, 60 pages, 3 eps figures, uses pstricks. Second version of Prepub. Institut Fourier 656 (Minor modifications in the abstract and in the introduction.)

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