Meridional Rank of Knots Whose Exterior is a Graph Manifold

preprint2016arXivOpen access

Abstract

We prove for a large class of knots that the meridional rank coincides with the bridge number. This class contains all knots whose exterior is a graph manifold. This gives a partial answer to a question of S. Cappell and J. Shaneson, see problem 1.11 on Kirby's list.

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