Thinning with a forked extended Scharlemann cycle and a bigon or trigon

uploaded by: Ken Baker on July 29, 2008

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Assume non integral surgery on a knot in S^3 produces a knot in a manifold M such that the knot has a 2 bridge presentation with respect to a fixed Heegaard surface. Give a forked extended Scharlemann cycle on the graph of intersection on the Heegaard sphere sharing a certain edge with another bigon or trigon, there is an isotopy that makes the knot 1 bridge. This model gives the construction of a complex in M along which the isotopy occurs. This is a situation that arises in an upcoming article...

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