Refined Kirby calculus for integral homology spheres
Geometric Topology
2009-03-01 v2 Quantum Algebra
Abstract
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.
Cite
@article{arxiv.math/0509039,
title = {Refined Kirby calculus for integral homology spheres},
author = {Kazuo Habiro},
journal= {arXiv preprint arXiv:math/0509039},
year = {2009}
}
Comments
This is the version published by Geometry & Topology on 18 September 2006