English

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

R2 v1 2026-07-22T18:01:16.878Z