On surgery along Brunnian links in 3–manifolds

Abstract

We consider surgery moves along .n C 1/-component Brunnian links in compact connected oriented 3-manifolds, where the framing of the components is in f 1 k ; k 2 Zg. 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.