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arXiv · 1006.1026

Non-minimal bridge positions of torus knots are stabilized

Makoto Ozawa
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Abstract

We show that any non-minimal bridge decomposition of a torus knot is stabilized and that $n$-bridge decompositions of a torus knot are unique for any integer $n$. 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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Makoto Ozawa. 2010-06-05. Non-minimal bridge positions of torus knots are stabilized. https://doi.org/10.1017/s0305004111000235

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