On surgery along Brunnian links in 3–manifolds

Meilhan, Jean-Baptiste

doi:10.2140/agt.2006.6.2417

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On surgery along Brunnian links in $3$–manifolds

Jean-Baptiste Meilhan

Algebraic & Geometric Topology 6 (2006) 2417–2453

DOI: 10.2140/agt.2006.6.2417

arXiv: math.GT/0603421

Abstract

We consider surgery moves along $(n + 1)$ –component Brunnian links in compact connected oriented $3$ –manifolds, where the framing of the components is in ${\frac{1}{k}; k \in Z}$ . We show that no finite type invariant of degree $< 2 n - 2$ 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

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M27

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Publication

Received: 30 May 2006

Accepted: 14 November 2006

Published: 13 December 2006

Authors

Jean-Baptiste Meilhan
Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502 Japan

Volume 6, issue 5 (2006)