Non-minimal bridge positions of torus knots are stabilized

Details Non-minimal bridge positions of torus knots are stabilized Non-minimal bridge positions of torus knots are stabilized

2010-06-05

arxiv.org/abs/1006.1026v1

Mathematics

Geometric Topology

11 pages, 4 figures

Scientific paper

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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