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

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

1998-06-20

arxiv.org/abs/math/9806113v1

Mathematics

Geometric Topology

To appear in "Topology and its Applications" (8 pages, 9 figures) see http://www.math.ohio-state.edu/~kerler/papers/KC/

Scientific paper

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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