Non-minimal bridge positions of torus knots are stabilized

preprint2010arXivOpen access

Abstract

We show that any non-minimal bridge decomposition of a torus knot is stabilized and that nn-bridge decompositions of a torus knot are unique for any integer nn. This implies that a knot in a bridge position is a torus knot if and only if there exists a torus containing the knot such that it intersects the bridge sphere in two essential loops.

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