Algebraic & Geometric Topology

On surgery along Brunnian links in $3$–manifolds

Jean-Baptiste Meilhan

Full-text: Open access

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 {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

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

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

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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