Kirby Calculus in Manifolds with Boundary

  title={Kirby Calculus in Manifolds with Boundary},
  author={Justin Roberts},
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 [K1] gives the answer when the manifold is S 3 , and Fenn and Rourke [FR] extended it to the case of any closed orientable 3-manifold, or S 1 ˜ ×S 2. The purpose of this note is to give the answer in the general… CONTINUE READING

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