Refined Kirby calculus for integral homology spheres

Details Refined Kirby calculus for integral homology spheres Refined Kirby calculus for integral homology spheres

2005-09-02

arxiv.org/abs/math/0509039v2

Geom. Topol. 10 (2006) 1285-1317

Mathematics

Geometric Topology

This is the version published by Geometry & Topology on 18 September 2006

Scientific paper

10.2140/gt.2006.10.1285

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 +/-1-framed links with zero linking numbers.

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