Refined Kirby calculus for integral homology spheres

Habiro, Kazuo¹

¹ Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606–8502, Japan

Geometry & topology, Tome 10 (2006) no. 3, pp. 1285-1317.

Résumé

A theorem of Kirby states that two framed links in the $3$–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 $\pm 1$–framed links with zero linking numbers.

Détail

DOI : 10.2140/gt.2006.10.1285

Keywords: Kirby calculus, framed link, surgery, handle-slide, integral homology sphere, band-slide, Hoste move

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