Stuck unknot

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In mathematics, a stuck unknot is a polygonal closed loop that is topologically the unknot but cannot be simplified to a planar polygon by rigid motions of the segments.[1][2] A related idea is to consider "stuck" polygonal open chains. Topologically these chains can be unknotted, but the limitation of using only rigid motions of the segments can create nontrivial knots in such a chain.

Consideration of such "stuck" configurations arises in the study of molecular chains in biochemistry.

References

  1. ↑ G. Aloupis, G. Ewald, and G. T. Toussaint, "More classes of stuck unknotted hexagons," Contributions to Algebra and Geometry, Vol. 45, No. 2, 2004, pp. 429–434.
  2. ↑ G. T. Toussaint, "A new class of stuck unknots in Pol-6," Contributions to Algebra and Geometry, Vol. 42, No. 2, 2001, pp. 301–306.
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