On surgery along Brunnian links in 3–manifolds

Meilhan, Jean-Baptiste¹

¹Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2417-2453

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 ∈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.

Détail

DOI : 10.2140/agt.2006.6.2417

Keywords: 3-manifolds, finite type invariants, Brunnian links, Goussarov-Vassiliev invariants, claspers

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