Algebraic & Geometric Topology

On surgery along Brunnian links in $3$–manifolds

Jean-Baptiste Meilhan

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We consider surgery moves along (n+1)–component Brunnian links in compact connected oriented 3–manifolds, where the framing of the components is in {1k  ; kZ}. We show that no finite type invariant of degree <2n2 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.

Article information

Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2417-2453.

Received: 30 May 2006
Accepted: 14 November 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M27: Invariants of knots and 3-manifolds

3-manifolds finite type invariants Brunnian links Goussarov-Vassiliev invariants claspers


Meilhan, Jean-Baptiste. On surgery along Brunnian links in $3$–manifolds. Algebr. Geom. Topol. 6 (2006), no. 5, 2417--2453. doi:10.2140/agt.2006.6.2417.

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