Volume 6, issue 5 (2006)

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On surgery along Brunnian links in $3$–manifolds

Jean-Baptiste Meilhan

Algebraic & Geometric Topology 6 (2006) 2417–2453
 arXiv: math.GT/0603421
Abstract

We consider surgery moves along $\left(n+1\right)$–component Brunnian links in compact connected oriented $3$–manifolds, where the framing of the components is in . 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.

Keywords
3-manifolds, finite type invariants, Brunnian links, Goussarov-Vassiliev invariants, claspers
Primary: 57N10
Secondary: 57M27