Kirby calculus in manifolds with boundary
Geometric Topology
2007-05-23 v1
Abstract
Suppose there are two framed links in a compact, connected 3-manifold (possibly with boundary, or non-orientable) such that the associated 3-manifolds obtained by surgery are homeomorphic (relative to their common boundary, if there is one.) How are the links related? Kirby's theorem gives the answer when the manifold is S^3, and Fenn and Rourke extended it to the case of any closed orientable 3-manifold, or twisted S^1 cross S^2. The purpose of this note is to give the answer in the general case, using only minor modifications of Kirby's original proof.
Keywords
Cite
@article{arxiv.math/9812086,
title = {Kirby calculus in manifolds with boundary},
author = {Justin Roberts},
journal= {arXiv preprint arXiv:math/9812086},
year = {2007}
}
Comments
7 pages, 5 figures using epsf