Stuck unknot

In mathematics, a stuck unknot is a closed polygonal chain that is topologically to the unknot but cannot be deformed to a simple polygon by rigid motions of the segments.^[1][2] Similarly a stuck open chain is an open polygonal chain such that the segments may not be aligned by moving rigidly its segments. Topologically such a chain 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.