Splitting formulae for the Kontsevich-Kuperberg-Thurston invariant of rational homology 3-spheres

Christine Lescop (1)

1 IF - Institut Fourier

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.

Mots clés: 3-manifolds; configuration space integrals; homology spheres; finite type invariants; Jacobi diagrams; clovers; claspers; Casson-Walker invariant

Domaines: Topologie géométrique [math.GT]

Christine Lescop. Splitting formulae for the Kontsevich-Kuperberg-Thurston invariant of rational homology 3-spheres. 2004. ⟨hal-00381903⟩