On surgery along Brunnian links in 3-manifolds

Details On surgery along Brunnian links in 3-manifolds On surgery along Brunnian links in 3-manifolds

2006-03-17

arxiv.org/abs/math/0603421v3

Algebr. Geom. Topol. 6 (2006) 2417-2453

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 13 December 2006

Scientific paper

10.2140/agt.2006.6.2417

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.

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