## Geometry & Topology

### Refined Kirby calculus for integral homology spheres

Kazuo Habiro

#### 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.

#### Article information

Source
Geom. Topol., Volume 10, Number 3 (2006), 1285-1317.

Dates
Accepted: 20 June 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799765

Digital Object Identifier
doi:10.2140/gt.2006.10.1285

Mathematical Reviews number (MathSciNet)
MR2255498

Zentralblatt MATH identifier
1130.57028

#### Citation

Habiro, Kazuo. Refined Kirby calculus for integral homology spheres. Geom. Topol. 10 (2006), no. 3, 1285--1317. doi:10.2140/gt.2006.10.1285. https://projecteuclid.org/euclid.gt/1513799765

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