On surgery along Brunnian links in 3-manifolds
Résumé
We consider surgery moves along (n+1)-component Brunnian links in compact connected oriented 3-manifolds, where the framing of the components is in {1/k ; k in Z}. We show that no finite type invariant of degree < 2n-2 can detect such a surgery move. The case of two link-homotopic Brunnian links is also considered. We relate finite type invariants of integral homology spheres obtained by such operations to Goussarov-Vassiliev invariants of Brunnian links.