## Algebraic & Geometric Topology

### On surgery along Brunnian links in $3$–manifolds

Jean-Baptiste Meilhan

#### 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 . 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.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796642

Digital Object Identifier
doi:10.2140/agt.2006.6.2417

Mathematical Reviews number (MathSciNet)
MR2286031

Zentralblatt MATH identifier
1128.57021

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796642

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