Abstract
A theorem of Kirby states that two framed links in the –sphere produce orientation-preserving homeomorphic results of surgery if they are related by a sequence of stabilization and handle-slide moves. The purpose of the present paper is twofold: First, we give a sufficient condition for a sequence of handle-slides on framed links to be able to be replaced with a sequences of algebraically canceling pairs of handle-slides. Then, using the first result, we obtain a refinement of Kirby’s calculus for integral homology spheres which involves only –framed links with zero linking numbers.
Citation
Kazuo Habiro. "Refined Kirby calculus for integral homology spheres." Geom. Topol. 10 (3) 1285 - 1317, 2006. https://doi.org/10.2140/gt.2006.10.1285
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