Volume 6, issue 5 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 (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.

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