On Kirby calculus for null-homotopic framed links in 3-manifolds
Geometric Topology
2014-10-01 v2
Abstract
Kirby proved that two framed links in S^3 give orientation-preserving homeomorphic results of surgery if and only if these two links are related by a sequence of two kinds of moves called stabilizations and handle-slides. Fenn and Rourke gave a necessary and sufficient condition for two framed links in a closed, oriented 3-manifold to be related by a finite sequence of these moves. The purpose of this paper is twofold. We first give a generalization of Fenn and Rourke's result to 3-manifolds with boundary. Then we apply this result to the case of framed links whose components are null-homotopic in the 3-manifold.
Keywords
Cite
@article{arxiv.1302.0612,
title = {On Kirby calculus for null-homotopic framed links in 3-manifolds},
author = {Kazuo Habiro and Tamara Widmer},
journal= {arXiv preprint arXiv:1302.0612},
year = {2014}
}
Comments
16 pages, 5 figures. With minor corrections. To appear in Algebraic and Geometric Topology