Splitting formulae for the Kontsevich-Kuperberg-Thurston invariant of   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 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. 
Christine Lescop (CNRS, Institut Fourier, Grenoble)