Turkish Journal of Mathematics
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 S^1 \tilde{\times} 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.
DOI
-
First Page
111
Last Page
117
Recommended Citation
ROBERTS, Justin (1997) "Kirby Calculus in Manifolds with Boundary," Turkish Journal of Mathematics: Vol. 21: No. 1, Article 11. Available at: https://journals.tubitak.gov.tr/math/vol21/iss1/11
