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On Kirby calculus for
null-homotopic framed links in $3$–manifolds
Kazuo Habiro and Tamara Widmer |
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Algebraic & Geometric Topology 14 (2014) 115–134
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Abstract |
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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. |
Keywords
$3$–manifold, framed link, surgery, Kirby calculus,
null-homotopic link
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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References |
Publication
Received: 23 February 2013
Revised: 19 June 2013
Accepted: 21 June 2013
Preview posted: 21 November 2013
Published: 9 January 2014
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Authors |
| Kazuo Habiro | |
| Research Institute for Mathematical
Sciences Kyoto University Kyoto 606-8502 Japan |
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| Tamara Widmer | |
| Institut für Mathematik Universität Zürich Winterthurerstr. 190 CH-8057 Zürich Switzerland |
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