Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 1 (2014), 115-134.
On Kirby calculus for null-homotopic framed links in $3$–manifolds
Kirby proved that two framed links in give orientation-preserving homeomorphic results of surgery if and only if these two links are related by a sequence of two kinds of moves called stabilizations and handle-slides. Fenn and Rourke gave a necessary and sufficient condition for two framed links in a closed, oriented –manifold to be related by a finite sequence of these moves.
The purpose of this paper is twofold. We first give a generalization of Fenn and Rourke’s result to –manifolds with boundary. Then we apply this result to the case of framed links whose components are null-homotopic in the –manifold.
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 115-134.
Received: 23 February 2013
Revised: 19 June 2013
Accepted: 21 June 2013
First available in Project Euclid: 19 December 2017
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Habiro, Kazuo; Widmer, Tamara. On Kirby calculus for null-homotopic framed links in $3$–manifolds. Algebr. Geom. Topol. 14 (2014), no. 1, 115--134. doi:10.2140/agt.2014.14.115. https://projecteuclid.org/euclid.agt/1513715796