On surgery along Brunnian links in 3-manifolds
arXiv:math/0603421 · doi:10.2140/agt.2006.6.2417
Abstract
We consider surgery moves along (n+1)-component Brunnian links in compact connected oriented 3-manifolds, where the framing of the each component is 1/k for 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.
This is the version published by Algebraic & Geometric Topology on 13 December 2006