Equivalence of a Bridged Link Calculus and Kirby's Calculus on Non-Simply Connected 3-Manifolds

Thomas Kerler

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Equivalence of a Bridged Link Calculus and Kirby's Calculus on Non-Simply Connected 3-Manifolds

Thomas Kerler

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Abstract

We recall an extension of Kirby's Calculus on non-simply connected 3-manifolds given in [FR], and the surgery calculus of bridged links from [Ke], which involves only local moves. We give a short combinatorial proof that the two calculi are equivalent, and thus describe the same classes of 3-manifolds. This makes the proofs for the validity of surgery calculi in [FR] and [Ke] interchangeable.

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Thomas Kerler. 1998-06-20. Equivalence of a Bridged Link Calculus and Kirby's Calculus on Non-Simply Connected 3-Manifolds. https://arxiv.org/abs/math/9806113

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