Unknot diagrams requiring a quadratic number of Reidemeister moves to untangle

Details Unknot diagrams requiring a quadratic number of Reidemeister moves to untangle Unknot diagrams requiring a quadratic number of Reidemeister moves to untangle

2007-11-15

arxiv.org/abs/0711.2350v1

Mathematics

Geometric Topology

Scientific paper

We present a sequence of diagrams of the unknot for which the minimum number
of Reidemeister moves required to pass to the trivial diagram is quadratic with
respect to the number of crossings. These bounds apply both in $S^2$ and in
$\R^2$.

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