Abstract
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.
Citation
Kazuo Habiro. Tamara Widmer. "On Kirby calculus for null-homotopic framed links in $3$–manifolds." Algebr. Geom. Topol. 14 (1) 115 - 134, 2014. https://doi.org/10.2140/agt.2014.14.115
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