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

  • Author(s): Hass, Joel
  • Nowik, Tahl
  • et al.

Published Web Location

https://arxiv.org/pdf/0711.2350.pdf
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Abstract

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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