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arXiv · 1302.0612

On Kirby calculus for null-homotopic framed links in 3-manifolds

Kazuo Habiro·Tamara Widmer
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Abstract

Kirby proved that two framed links in S^3 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 3-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 3-manifolds with boundary. Then we apply this result to the case of framed links whose components are null-homotopic in the 3-manifold.

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Kazuo Habiro, Tamara Widmer. 2013-06-23. On Kirby calculus for null-homotopic framed links in 3-manifolds. https://doi.org/10.2140/agt.2014.14.115

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